ملخص كتاب الفيزياء السادس العلمي 2016

1. ‫ﻓﺼﻮل‬ ‫ﻣﻠﺨﺼﺎت‬
‫اﻟﻔﻴﺰﻳﺎء‬
‫ﻟﻠﺼﻒ‬‫اﻟﺴﺎدس‬‫اﻟﻌﻠﻤﻲ‬
)‫وﻣﻼﺣﻈﺎت‬ ‫ﻗﻮاﻧﻴﻦ‬(
‫إﻋﺪاد‬
‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬ ‫اﻟﻔﻴﺰﻳﺎء‬ ‫ﻣﺪرس‬
email/abuhussen_72@yahoo.com
www.facebook.com/saeedmuhi
2015 – 2016

2. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-3-
‫ﺴﻌﺔ‬ ‫اﻟﻤﺘ‬:‫ﺎز‬‫ﺟﮭ‬ ‫ﻦ‬ ‫ﻋ‬ ‫ﺎرة‬‫ﻋﺒ‬ ‫ﻲ‬ ‫ھ‬‫ﺄﻟﻒ‬ ‫ﯾﺘ‬‫زوج‬ ‫ﻦ‬ ‫ﻣ‬)‫او‬‫ﺮ‬‫أﻛﺜ‬(‫ﺮ‬ ‫ﻏﯿ‬ ‫ﺪاءا‬ ‫اﺑﺘ‬ ‫ﺎزل‬‫ﻋ‬ ‫ﺎ‬ ‫ﺑﯿﻨﮭﻤ‬ ‫ﺼﻞ‬ ‫ﯾﻔ‬ ‫ﻠﺔ‬ ‫اﻟﻤﻮﺻ‬ ‫ﺼﻔﺎﺋﺢ‬ ‫اﻟ‬ ‫ﻦ‬ ‫ﻣ‬
‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫واﻟﻄﺎﻗﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫اﻟﺸﺤﻨﺎت‬ ‫ﻟﺘﺨﺰﯾﻦ‬ ‫ﺗﺴﺘﻌﻤﻞ‬ ‫ﻣﺸﺤﻮﻧﺘﯿﻦ‬.
‫ﺑﺎﻟﺮﻣﺰ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫اﻟﺪواﺋﺮ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫وﯾﺮﻣﺰ‬‫او‬‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﺟﻤﯿﻊ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺮﻣﺰ‬ ‫ھﺬا‬ ‫وﯾﻨﻄﺒﻖ‬.
‫اﻟﻤﺘﻮازﻳﺘﻴﻦ‬ ‫اﻟﺼﻔﻴﺤﺘﻴﻦ‬ ‫ذات‬ ‫اﻟﻤﺘﺴﻌﺔ‬:
‫ﻀﮭﻤﺎ‬ ‫ﺑﻌ‬ ‫ﻦ‬ ‫ﻋ‬ ‫ﺰوﻟﺘﯿﻦ‬ ‫ﻣﻌ‬ ‫ﺎﺛﻠﺘﯿﻦ‬ ‫ﻣﺘﻤ‬ ‫ﺴﺘﻮﯾﺘﯿﻦ‬ ‫ﻣ‬ ‫ﻠﺘﯿﻦ‬ ‫ﻣﻮﺻ‬ ‫ﻔﯿﺤﺘﯿﻦ‬ ‫ﺻ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﻮازﯾﺘﯿﻦ‬ ‫اﻟﻤﺘ‬ ‫ﺼﻔﯿﺤﺘﯿﻦ‬ ‫اﻟ‬ ‫ذات‬ ‫ﺴﻌﺔ‬ ‫اﻟﻤﺘ‬ ‫ﺎﻟﻒ‬ ‫ﺗﺘ‬
‫ﺎ‬‫ﻣﻨﮭﻤ‬ ‫ﻞ‬‫ﻛ‬ ‫وﻣﺴﺎﺣﺔ‬ ‫وﻣﺘﻮازﯾﺘﯿﻦ‬)A(‫ﺪ‬‫ﺑﺎﻟﺒﻌ‬ ‫ﻀﮭﻤﺎ‬‫ﺑﻌ‬ ‫ﻦ‬‫ﻋ‬ ‫ﺪان‬‫وﺗﺒﻌ‬)d(‫ﺼﻔﯿﺤﺘﯿﻦ‬‫اﻟ‬ ‫ﻮن‬‫ﺗﻜ‬‫ﺸﺤﻮﻧﺘﯿﻦ‬‫ﻣ‬ ‫ﺮ‬‫ﻏﯿ‬ ‫ﺪاءا‬‫اﺑﺘ‬‫ﺪ‬‫وﺑﻌ‬
‫ﻧﻮﻋﺎ‬ ‫وﻣﺨﺘﻠﻔﺘﯿﻦ‬ ‫ﻣﻘﺪارا‬ ‫ﻣﺘﺴﺎوﯾﺘﯿﻦ‬ ‫ﺷﺤﻨﺘﯿﻦ‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﻋﻠﻰ‬ ‫ﺗﻈﮭﺮ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺷﺤﻦ‬.
♦‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺷﺤﻦ‬ ‫ﯾﺘﻢ‬ ‫ان‬ ‫ﺑﻌﺪ‬‫ﻮازﯾﺘﯿﻦ‬‫اﻟﻤﺘ‬ ‫ﺼﻔﯿﺤﺘﯿﻦ‬‫اﻟ‬ ‫ذات‬‫ﻰ‬‫اﻻﻋﻠ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ذات‬ ‫ﺼﻔﯿﺤﺔ‬‫اﻟ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺎﺋﻲ‬‫ﻛﮭﺮﺑ‬ ‫ﺪ‬‫ﺟﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﺪ‬‫ﯾﺘﻮﻟ‬
)‫اﻟﻤﻮﺟﺐ‬ ‫اﻟﺠﮭﺪ‬(‫اﻻوطﺎ‬ ‫اﻟﺠﮭﺪ‬ ‫ذات‬ ‫واﻟﺼﻔﯿﺤﺔ‬)‫اﻟﺴﺎﻟﺐ‬ ‫اﻟﺠﮭﺪ‬(‫و‬‫ﺑﺎﻟﺮﻣﺰ‬ ‫ﻟﮫ‬ ‫ﯾﺮﻣﺰ‬)V∆(.
♦‫و‬‫و‬ ‫ﻗﺪ‬‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﺪار‬‫ﻣﻘ‬ ‫ﻊ‬‫ﻣ‬ ‫ﺎ‬‫طﺮدﯾ‬ ‫ﺐ‬‫ﯾﺘﻨﺎﺳ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﻓﺮق‬ ‫ان‬ ‫ﻋﻤﻠﯿﺎ‬ ‫ﺟﺪ‬)Q(‫ﻦ‬‫ﻣ‬ ‫أي‬ ‫ﻲ‬‫ﻓ‬ ‫ﺔ‬‫اﻟﻤﺨﺘﺰﻧ‬
‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬.
‫ان‬ ‫أي‬:
ttancons
V
Q
Q.
ttancons
1
VQV =
∆
⇒=∆⇒α∆
‫اﻟﺜﺎﺑﺖ‬ ‫واﻟﻤﻘﺪار‬)constant(‫ﺎﻟﺮﻣﺰ‬‫ﺑ‬ ‫ﺎ‬‫ﻟﮭ‬ ‫ﺰ‬‫وﯾﺮﻣ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻌﺔ‬‫ﺳ‬ ‫ﯾﺴﻤﻰ‬)C(.‫اﻟﻌ‬ ‫ﻮن‬‫ﯾﻜ‬ ‫ﺪﻣﺎ‬‫وﻋﻨ‬ ‫ﺬﻟﻚ‬‫ﻟ‬‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺎزل‬
‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﻓﺎن‬ ‫اﻟﮭﻮاء‬ ‫او‬ ‫اﻟﻔﺮاغ‬ ‫اﻟﻤﺘﺴﻌﺔ‬)C(‫ﻔﯿﺤﺘﯿﮭﺎ‬‫ﺻ‬ ‫ﻣﻦ‬ ‫أي‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫واﻟﺸﺤﻨﺔ‬)Q(‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫وﻓ‬
‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬)V∆(‫اﻟﺘﺎﻟﻲ‬ ‫ﺑﺎﻟﺸﻜﻞ‬ ‫ﺗﻜﺘﺐ‬:
♦‫و‬ ‫ﺎراد‬‫ﺑﺎﻟﻔ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻌﺔ‬‫ﺳ‬ ‫ﺎس‬‫ﺗﻘ‬‫ﺰه‬‫رﻣ‬)F(‫ﺰه‬‫ورﻣ‬ ‫ﺎﻟﻜﻮﻟﻮم‬‫ﺑ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﺎس‬‫وﺗﻘ‬ ‫ﺰاءه‬‫اﺟ‬ ‫او‬)C(‫ﺰاءه‬‫اﺟ‬ ‫او‬‫ﺮق‬‫ﻓ‬ ‫ﺎس‬‫وﯾﻘ‬
‫ورﻣﺰه‬ ‫ﺑﺎﻟﻔﻮﻟﻂ‬ ‫اﻟﺠﮭﺪ‬)V(‫ﻟﺬﻟﻚ‬)F=C/V. (
♦‫ﻮم‬ ‫اﻟﻜﻮﻟ‬ ‫ﺰاء‬ ‫اﺟ‬ ‫او‬ ‫ﺎراد‬ ‫اﻟﻔ‬ ‫ﺰاء‬ ‫اﺟ‬‫ﻲ‬ ‫اﻟﻤﻠ‬ ‫ﻲ‬ ‫ھ‬)m(‫ﺎﯾﻜﺮو‬ ‫واﻟﻤ‬)µ(‫ﺎﻧﻮ‬ ‫واﻟﻨ‬)n(‫ﻮ‬ ‫واﻟﺒﯿﻜ‬)P(‫ﺰاء‬ ‫اﻻﺟ‬ ‫ﺬه‬ ‫ھ‬ ‫ﺴﻤﻰ‬ ‫وﺗ‬
‫اﻟﻘﯿﺎس‬ ‫ﺑﺎدﺋﺎت‬‫ﺣﯿﺚ‬:
m=10-3
, µ=10-6
, n=10-9
, p=10-12
♦‫اﻟﺘﻌﺮﯾﻒ‬ ‫ﺑﻤﻮﺟﺐ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻗﺎﻧﻮن‬ ‫اﺳﺘﺨﺪام‬ ‫ﺣﺎل‬ ‫ﻓﻲ‬)
V
Q
C
∆
=(‫ﺪة‬‫اﻟﻮﺣ‬ ‫ﻰ‬‫اﻟ‬ ‫اﻟﺒﺎدﺋﺔ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻮﯾﻞ‬ ‫اﻟﻀﺮوري‬ ‫ﻣﻦ‬ ‫ﻟﯿﺲ‬
‫اﻟﺸﺤﻨﺔ‬ ‫ﺑﺎدﺋﺔ‬ ‫ھﻲ‬ ‫اﻟﺴﻌﺔ‬ ‫وﺑﺎدﺋﺔ‬ ‫اﻟﺴﻌﺔ‬ ‫ﺑﺎدﺋﺔ‬ ‫ھﻲ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺑﺎدﺋﺔ‬ ‫ﺗﻜﻮن‬ ‫ان‬ ‫ﺑﺸﺮط‬.
‫س‬/‫اﻻﺳﺎﺳﯿﺔ‬ ‫ﺑﺎﻟﻮﺣﺪات‬ ‫اﻟﻔﺎراد‬ ‫اﺷﺘﻖ‬.
‫ج‬/
2
22
2
222
m.kg
s.C
m.
s
m
.kg
C
m.N
C
J
C
C
J
C
V
C
F ======
‫ﺍﳌﺘﺴﻌﺔ‬ ‫ﺻﻔﻴﺤﺘﻲ‬ ‫ﺑﲔ‬ ‫ﺍﻟﻜﻬﺮﺑﺎﺋﻲ‬ ‫ﺎﻝ‬‫ﺍ‬:‫ﻧﺴﺒﺔ‬ ‫ھﻮ‬‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬)V∆(‫ﺪ‬‫اﻟﺒﻌ‬ ‫ﻰ‬‫إﻟ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬)d(‫ﯿﻦ‬‫ﺑ‬
‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬.
‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬‫اﻟﻤﺠ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﻓﺎن‬ ‫ھﻮاء‬ ‫او‬ ‫ﻓﺮاغ‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻌﺎزل‬ ‫ﯾﻜﻮن‬ ‫وﻋﻨﺪﻣﺎ‬ ‫اﻟﺘﻌﺮﯾﻒ‬ ‫ھﺬا‬ ‫وﺑﻤﻮﺟﺐ‬ ‫ﻟﺬﻟﻚ‬)E(
‫اﻟﺠﮭﺪ‬ ‫وﻓﺮق‬)V∆(‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫واﻟﺒﻌﺪ‬)d(‫ھﻲ‬:
)‫ﻫﻮاء‬ ‫او‬ ‫ﻓﺮاغ‬ ‫اﻟﺼﻔﻴﺤﺘﻴﻦ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻌﺎزل‬ ‫ﻛﺎن‬ ‫اذا‬(
d
V
E
∆
=
V
Q
C
∆
=
‫ﻧﯿﻮﺗﻦ‬ ‫ھﻲ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫وﺣﺪة‬‫ﻛﻮﻟﻮم‬)N/C(‫ﻓﻮﻟﻂ‬ ‫او‬‫ﻣﺘﺮ‬)v/m(

3. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-4-
‫ﻓﺎن‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ھﺬه‬ ‫إﻟﻰ‬ ‫اﺳﺘﻨﺎدا‬:
1(‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬‫اﻟﻤﺠ‬)E(‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﻊ‬‫ﻣ‬ ‫ﺎ‬‫طﺮدﯾ‬ ‫ﺐ‬‫ﯾﺘﻨﺎﺳ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬)∆V(‫ﺼﻔﯿﺤﺘﯿﻦ‬‫اﻟ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺪ‬‫اﻟﺒﻌ‬ ‫ﻮت‬‫ﺑﺜﺒ‬
‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬ ‫اﻟﺒﻌﺪ‬ ‫ﻣﻊ‬ ‫ﻋﻜﺴﯿﺎ‬ ‫وﺗﻨﺎﺳﺒﺎ‬‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﺠﮭﺪ‬.
‫ﻟﺬﻟﻚ‬:
E α ∆V ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺒﻌﺪ‬ ‫ﺑﺜﺒﻮت‬
E α
d
1
‫ﺑﺎﻟﺒﻄﺎرﯾﺔ‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﯾﺜﺒﺖ‬ ‫ﺣﯿﺚ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬
2(‫ﻛ‬ ‫ﻛﺎن‬ ‫إذا‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ﯾﺜﺒﺖ‬‫واﺣﺪ‬ ‫ان‬ ‫ﻓﻲ‬ ‫ﻣﺘﻐﯿﺮﯾﻦ‬ ‫او‬ ‫ﺛﺎﺑﺘﯿﻦ‬ ‫واﻟﺒﻌﺪ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻣﻦ‬ ‫ﻞ‬.
‫ﻟﻠﻤﺘﺴﻌﺔ‬ ‫ﺍﻟﻜﻬﺮﺑﺎﺋﻲ‬ ‫ﺎﻝ‬‫ﺍ‬ ‫ﰲ‬ ‫ﺍﳌﺨﺘﺰﻧﺔ‬ ‫ﺍﻟﻄﺎﻗﺔ‬ ‫ﺣﺴﺎﺏ‬:
♦‫ﺔ‬‫اﻟﻄﺮدﯾ‬ ‫ﺔ‬‫اﻟﻌﻼﻗ‬ ‫ﺢ‬‫ﯾﻮﺿ‬ ‫ﺎﻧﻲ‬‫ﺑﯿ‬ ‫ﻂ‬‫ﻣﺨﻄ‬ ‫ﻢ‬‫رﺳ‬ ‫ﻼل‬‫ﺧ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺘﺴﻌﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﺣﺴﺎب‬ ‫ﯾﻤﻜﻦ‬
‫اﻟﺸﺤﻨﺔ‬ ‫ﺑﯿﻦ‬)Q(‫وﻓﺮق‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﻣﻦ‬ ‫أي‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫اﻟﺠﮭﺪ‬)∆V(‫ﺎ‬‫ﺑﯿﻨﮭﻤ‬.‫ﺴﺎب‬‫ﺣ‬ ‫ﻼل‬‫ﺧ‬ ‫ﻦ‬‫وﻣ‬
‫اﻟﻤﺜﻠﺚ‬ ‫ﻣﺴﺎﺣﺔ‬)‫اﻟﻤﺜﻠﺚ‬ ‫ﻣﺴﺎﺣﺔ‬=
2
1
‫اﻟﻘﺎﻋﺪة‬×‫اﻻرﺗﻔﺎع‬(
‫ﺪة‬ ‫اﻟﻘﺎﻋ‬ ‫ﺚ‬‫ﺣﯿ‬)‫ﻞ‬‫ﺗﻤﺜ‬∆V(‫ﺎع‬ ‫اﻻرﺗﻔ‬ ،)‫ﺸﺤﻨﺔ‬ ‫اﻟ‬ ‫ﺪار‬ ‫ﻣﻘ‬ ‫ﻞ‬‫ﯾﻤﺜ‬Q(‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬ ‫اﻟﻤﺠ‬ ‫ﻲ‬ ‫ﻓ‬ ‫ﺔ‬ ‫اﻟﻤﺨﺘﺰﻧ‬ ‫ﺔ‬ ‫اﻟﻄﺎﻗ‬ ‫ﺴﺎب‬ ‫ﺣ‬ ‫ﻦ‬ ‫ﯾﻤﻜ‬
‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫ﻟﻠﻤﺘﺴﻌﺔ‬:
‫ﺎﻟﺠﻮل‬‫ﺑ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﺗﻘﺎس‬)J(‫ﺎﻟﻜﻮﻟﻮم‬‫ﺑ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﻮن‬‫ﺗﻜ‬ ‫ﺪﻣﺎ‬‫ﻋﻨ‬)C(‫ﺎﻟﻔﻮﻟﻂ‬‫ﺑ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫وﻓ‬)V(
‫ﺑﺎﻟﻔﺎرد‬ ‫واﻟﺴﻌﺔ‬)F. (
‫اﻟﺘﺎﻟﯿﺔ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﻣﻦ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫اﻟﻘﺪرة‬ ‫ﺣﺴﺎب‬ ‫ﯾﻤﻜﻦ‬ ‫ﻛﺬﻟﻚ‬:
‫اﻟﻘﺪر‬ ‫ﻗﯿﺎس‬ ‫وﺣﺪة‬‫ﺑﺎﻟﺜﺎﻧﯿﺔ‬ ‫واﻟﺰﻣﻦ‬ ‫ﺑﺎﻟﺠﻮل‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬ ‫اﻟﻮاط‬ ‫ھﻲ‬ ‫ة‬.
‫ﻣﻼﺣﻈﺎﺕ‬/
v‫اﻟﻌﻼﻗﺔ‬ ‫ﻣﻦ‬:
Q.V
2
1
PE ∆=
‫ﺮ‬‫ﻓ‬ ‫ﻊ‬‫ﻣ‬ ‫ﺎ‬‫طﺮدﯾ‬ ‫ﺐ‬‫ﺗﺘﻨﺎﺳ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬‫اﻟﻤﺠ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺔ‬‫اﻟﻤﺨﺘﺰﻧ‬ ‫ﺔ‬‫اﻟﻄﺎﻗ‬ ‫ان‬ ‫ﺪ‬‫ﻧﺠ‬‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﻮت‬‫ﺑﺜﺒ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ق‬
‫ﻣﻊ‬ ‫طﺮدﯾﺎ‬ ‫وﺗﺘﻨﺎﺳﺐ‬‫ﻣ‬ ‫طﺮدﯾﺎ‬ ‫وﺗﺘﻨﺎﺳﺐ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬ ‫اﻟﺸﺤﻨﺔ‬‫اﻟﺴﻌﺔ‬ ‫ﺑﺜﺒﻮت‬ ‫واﻟﺸﺤﻨﺔ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻊ‬.
‫ان‬ ‫أي‬:
or
1
2
1
2
Q
Q
PE
PE
)constV(QPE =⇒=∆∝
C
Q
2
1
PEor)V(.C
2
1
PEorQ.V
2
1
PE
2
electric
2
electricelectric =∆=∆=
)t(time
PE
)P(Power electric
=
1
2
1
2
V
V
PE
PE
)constQ(VPE
∆
∆
=⇒=∆∝

4. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-5-
or
v‫اﻟﻌﻼﻗﺔ‬ ‫ﻣﻦ‬:
2
)V(.C
2
1
PE ∆=
‫ﻣﻊ‬ ‫طﺮدﯾﺎ‬ ‫ﺗﺘﻨﺎﺳﺐ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ان‬ ‫ﻧﺠﺪ‬‫ﻊ‬‫ﻣﺮﺑ‬‫ﺴﻌﺔ‬‫اﻟ‬ ‫ﻮت‬‫ﺑﺜﺒ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫ﻓ‬
‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬ ‫اﻟﺴﻌﺔ‬ ‫ﻣﻊ‬ ‫طﺮدﯾﺎ‬ ‫وﺗﺘﻨﺎﺳﺐ‬‫اﻟﺸﺤﻨﺔ‬ ‫ﺑﺜﺒﻮت‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫وﻣﺮﺑﻊ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻣﻊ‬ ‫طﺮدﯾﺎ‬ ‫وﺗﺘﻨﺎﺳﺐ‬.
‫ان‬ ‫أي‬:
or
or
v‫اﻟﻌﻼﻗﺔ‬ ‫ﻣﻦ‬:
C
Q
2
1
PE
2
=
‫ﻧﺠﺪ‬‫ﺴﻌﺔ‬‫اﻟ‬ ‫ﻮت‬‫ﺑﺜﺒ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﻊ‬‫ﻣﺮﺑ‬ ‫ﻊ‬‫ﻣ‬ ‫ﺎ‬‫طﺮدﯾ‬ ‫ﺐ‬‫ﺗﺘﻨﺎﺳ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬‫اﻟﻤﺠ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺔ‬‫اﻟﻤﺨﺘﺰﻧ‬ ‫ﺔ‬‫اﻟﻄﺎﻗ‬ ‫ان‬
‫اﻟﺸﺤﻨﺔ‬ ‫ﺑﺜﺒﻮت‬ ‫اﻟﺴﻌﺔ‬ ‫ﻣﻊ‬ ‫ﻋﻜﺴﯿﺎ‬ ‫وﺗﺘﻨﺎﺳﺐ‬‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬ ‫اﻟﺴﻌﺔ‬ ‫ﻣﻊ‬ ‫وﻋﻜﺴﯿﺎ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﻣﺮﺑﻊ‬ ‫ﻣﻊ‬ ‫طﺮدﯾﺎ‬ ‫وﺗﺘﻨﺎﺳﺐ‬.
‫ان‬ ‫أي‬:
or
or
2
12
2
21
1
2
2
Q.C
Q.C
PE
PE
)constV(
C
Q
PE =⇒=∆∝
2
11
2
22
1
22
)V.(C
)V.(C
PE
PE
)constQ()V.(CPE
∆
∆
=⇒=∆∝
2
1
1
2
C
C
PE
PE
)constQ(
C
1
PE =⇒=∝
2
1
2
2
1
22
Q
Q
PE
PE
)constC(QPE =⇒=∝
1
2
1
2
C
C
PE
PE
)constV(CPE =⇒=∆∝
2
1
2
2
1
22
V
V
PE
PE
)constC(VPE
∆
∆
=⇒=∆∝
11
22
1
2
Q.V
Q.V
PE
PE
)constC(Q.VPE
∆
∆
=⇒=∆∝

5. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-6-
‫س‬/‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﺗﺼﺒﺢ‬ ‫اﻟﺴﻌﺔ‬ ‫ﺛﺎﺑﺘﺔ‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﯾﺘﻀﺎﻋﻒ‬ ‫ﻋﻨﺪﻣﺎ‬ ‫رﯾﺎﺿﯿﺎ‬ ‫اﺛﺒﺖ‬
‫؟‬ ‫اﻣﺜﺎل‬ ‫ارﺑﻌﺔ‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬
‫ج‬/
12
1111112
1212
222
PE4PE
)Q.V
2
1
(4)Q.V4(
2
1
)Q2).(V2(
2
1
PE
)ttanconsC(Q2QV2V
Q.V
2
1
PE
=∴
∆=∆=∆=∴
==⇒∆=∆
∆=
Q
‫س‬/‫ﺔ‬‫اﻟﺜﺎﻧﯿ‬ ‫ﻌﺔ‬‫ﺳ‬ ‫ﻊ‬‫رﺑ‬ ‫اﻻوﻟﻰ‬ ‫ﺳﻌﺔ‬ ‫ﻣﺘﺴﻌﺘﺎن‬‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﻌﻒ‬‫ﺿ‬ ‫ﻔﯿﺤﺘﯿﮭﺎ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫وﻓ‬
‫اﻟﺜﺎﻧﯿﺔ‬‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ﻣﻨﮭﻤﺎ‬ ‫ﻛﻞ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﺑﺎن‬ ‫اﺛﺒﺖ‬.
‫ج‬/
21
2
1
2
2
2
2
2
1
2
22
2
22
2
1
2121
2
22
2
11
2
1
2
22
2
11
2
1
PEPE1
PE
PE
)V(
)V(4
4
1
PE
PE
)V.(C
)V2.(C
4
1
PE
PE
V2V,C
4
1
C
)V.(C
)V.(C
PE
PE
)V.(C
2
1
)V.(C
2
1
PE
PE
=⇒=⇒
∆
∆×
=⇒
∆
∆
=∴
∆=∆=
∆
∆
=⇒
∆
∆
=
Q
‫ﺍﻟﻜﻬﺮﺑﺎﺋﻲ‬ ‫ﺍﻟﻌﺎﺯﻝ‬:)Dielectric(
‫ﻧﻮﻋﻴﻦ‬ ‫إﻟﻰ‬ ‫ﻛﻬﺮﺑﺎﺋﻴﺎ‬ ‫اﻟﻌﺎزﻟﺔ‬ ‫اﻟﻤﻮاد‬ ‫ﺗﺼﻨﻒ‬:
1-‫اﻟﻘﻄ‬ ‫اﻟﻌﻮازل‬‫ﺒﻴﺔ‬.2-‫اﻟﻘﻄﺒﻴﺔ‬ ‫ﻏﻴﺮ‬ ‫اﻟﻌﻮازل‬.
♦‫ﺳﯿﻜﻮن‬ ‫ﻋﺎزل‬ ‫ﻋﻠﻰ‬ ‫ﺗﺤﺘﻮي‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺤﺼﻞ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ﻓﺎن‬ ‫اﻟﻌﺎزل‬ ‫ﻧﻮﻋﻲ‬ ‫ﻛﻼ‬ ‫ﻓﻲ‬:
‫ﺣﯿﺚ‬:
Ek:، ‫اﻟﻌﺎزل‬ ‫ﺑﻮﺟﻮد‬ ‫اﻟﻤﺤﺼﻞ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬E:‫اﻟ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺆﺛﺮ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬‫اﻟﻔﺮاغ‬ ‫ﺑﻮﺟﻮد‬ ‫ﺼﻔﯿﺤﺘﯿﻦ‬
Ed:‫اﻟﻌﺎزل‬ ‫داﺧﻞ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬
‫اﻟﻤﺠﺎ‬ ‫ان‬ ‫أي‬‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺼﻞ‬‫اﻟﻤﺤ‬ ‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ل‬‫ﺴﻌﺔ‬‫ﻣﺘ‬‫ﺼﺪر‬‫اﻟﻤ‬ ‫ﻦ‬‫ﻋ‬ ‫ﺼﻠﺔ‬‫وﻣﻨﻔ‬ ‫ﺸﺤﻮﻧﺔ‬‫ﻣ‬)‫ﺔ‬‫اﻟﺒﻄﺎرﯾ‬(‫ﺴﺒﺔ‬‫ﺑﻨ‬ ‫ﻞ‬‫ﯾﻘ‬‫ﺖ‬‫ﺛﺎﺑ‬
‫اﻟﻌﺰل‬)k(‫ﻓﯿﻜﻮن‬:
dk EEE −= ‫ﯾﻜﻮ‬‫اﻷﺻﻠﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ﺑﺎﺗﺠﺎه‬ ‫اﻟﻤﺤﺼﻞ‬ ‫اﻟﻤﺠﺎل‬ ‫اﺗﺠﺎه‬ ‫ن‬

6. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-7-
‫و‬‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺔ‬‫اﻟﻌﻼﻗ‬ ‫ان‬ ‫ﺎ‬‫ﺑﻤ‬)V∆(‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬‫واﻟﻤﺠ‬)E(‫ﺼﻔﯿﺤﺘﯿﻦ‬‫اﻟ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺪ‬‫اﻟﺒﻌ‬ ‫ﻮت‬‫ﺑﺜﺒ‬ ‫ﺔ‬‫طﺮدﯾ‬)d(‫ﺎن‬‫ﻓ‬ ‫ﺬﻟﻚ‬‫ﻟ‬
‫ﺼﺪر‬ ‫اﻟﻤ‬ ‫ﻦ‬ ‫ﻋ‬ ‫ﺼﻠﺔ‬ ‫وﻣﻨﻔ‬ ‫ﺸﺤﻮﻧﺔ‬ ‫ﻣ‬ ‫ﺴﻌﺔ‬ ‫ﻣﺘ‬ ‫ﻔﯿﺤﺘﻲ‬ ‫ﺻ‬ ‫ﯿﻦ‬ ‫ﺑ‬ ‫ﺎزل‬ ‫اﻟﻌ‬ ‫ﺎل‬ ‫ادﺧ‬)‫ﺔ‬ ‫اﻟﺒﻄﺎرﯾ‬(‫ﺼﻔﯿﺤﺘﯿﻦ‬ ‫اﻟ‬ ‫ﯿﻦ‬ ‫ﺑ‬ ‫ﺪ‬ ‫اﻟﺠﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﯿﻘﻠﻞ‬ ‫ﺳ‬
)kV∆(‫ﺑﻨﺴﺒﺔ‬‫اﻟﻌﺰل‬ ‫ﺛﺎﺑﺖ‬)k(‫وﻛ‬ ‫اﻟﮭﻮاء‬ ‫او‬ ‫ﺑﺎﻟﻔﺮاغ‬ ‫ﻗﯿﻤﺘﮫ‬ ‫ﻋﻦ‬‫ﯾﻠﻲ‬ ‫ﻤﺎ‬:
k
kk
k V
k
Ed
d
V
k
E
d
V
E
d
V
E ∆=⇒
∆
=⇒
∆
=⇒
∆
=
‫ﻓﺎن‬ ‫ﻟﺬﻟﻚ‬:
‫وﺣﯿﺚ‬‫اﻟﺸﺤﻨﺔ‬ ‫ﻣﻘﺪار‬ ‫ﺛﺒﻮت‬ ‫ﻋﻨﺪ‬ ‫ﺻﻔﯿﺤﺘﯿﮭﺎ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺠﮭﺪ‬ ‫وﻓﺮق‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬ ‫ﺑﯿﻦ‬ ‫ﻋﻜﺴﯿﺔ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ان‬)‫ﺖ‬‫ﻛﺎﻧ‬ ‫اذا‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﺗﺜﺒﺖ‬
‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬(‫ﺎن‬‫ﻓ‬‫ﺎل‬‫إدﺧ‬‫ﯿﺆدي‬‫ﺳ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺎزل‬‫اﻟﻌ‬‫ﺎ‬‫زﯾ‬ ‫ﻰ‬‫إﻟ‬‫ﻌﺘﮭﺎ‬‫ﺳ‬ ‫دة‬‫ﺰل‬‫اﻟﻌ‬ ‫ﺖ‬‫ﺛﺎﺑ‬ ‫ﺴﺒﺔ‬‫ﺑﻨ‬
‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬)k(‫اﻟﻔﺮا‬ ‫ﺑﻮﺟﻮد‬ ‫ﺳﻌﺘﮭﺎ‬ ‫ﻋﻦ‬‫اﻟﮭﻮاء‬ ‫او‬ ‫غ‬.
V
Q
k
k
V
Q
V
Q
C
k
k
k
∆
=
∆
=
∆
=
‫ﻓﺎن‬ ‫ﻟﺬﻟﻚ‬:
‫ﺣﯿﺚ‬:
CK:‫اﻟﻌﺎزل‬ ‫ﺑﻮﺟﻮد‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬
C:‫اﻟﮭﻮاء‬ ‫او‬ ‫اﻟﻔﺮاغ‬ ‫ﺑﻮﺟﻮد‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬
k:‫اﻟﻌﺎزﻟﺔ‬ ‫ﻟﻠﻤﺎدة‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻌﺰل‬ ‫ﺛﺎﺑﺖ‬‫وھﻮ‬‫ﻟﻠﻤﺎدة‬ ‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﻤﺎﺣﯿﺔ‬‫اﻟﻮﺣﺪات‬ ‫ﻣﻦ‬ ‫ﻣﺠﺮد‬ ‫ﻋﺪد‬ ‫وھﻮ‬.
‫اﻟﻜﮫﺮﺑﺎﺋﻲ‬ ‫اﻟﻌﺰل‬ ‫ﺛﺎﺑﺖ‬)k: (‫ﻧﺴﺒﺔ‬ ‫ھﻮ‬‫ﻮ‬‫وھ‬ ‫اﻟﮭﻮاء‬ ‫او‬ ‫اﻟﻔﺮاغ‬ ‫ﺑﻮﺟﻮد‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬ ‫اﻟﻰ‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻮﺟﻮد‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬
‫اﻟﻌﺎزل‬ ‫ﻟﻠﻮﺳﻂ‬ ‫ﻣﻤﯿﺰة‬ ‫ﺻﻔﺔ‬.‫أن‬ ‫أي‬
‫ﻋﺎﺯﻝ‬ ‫ﺍﺩﺧﺎﻝ‬ ‫ﻋﻨﺪ‬‫ﻋﺰﻟﻪ‬ ‫ﺛﺎﺑﺖ‬)k(‫ﻓﺎﻥ‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﺻﻔﻴﺤﺘﻲ‬ ‫ﺑﲔ‬:
1-‫ﺰداد‬‫ﺗ‬ ‫ﻌﺘﮭﺎ‬‫ﺳ‬‫ﺰل‬‫اﻟﻌ‬ ‫ﺖ‬‫ﺛﺎﺑ‬ ‫ﺴﺒﺔ‬‫ﺑﻨ‬)k(‫ام‬ ‫ﺼﺪر‬ ‫ﺑﺎﻟﻤ‬ ‫ﺼﻠﺔ‬ ‫ﻣﺘ‬ ‫ﺎ‬‫ﻛﻮﻧﮭ‬ ‫ﻦ‬ ‫ﻋ‬ ‫ﺮ‬‫اﻟﻨﻈ‬ ‫ﺾ‬ ‫وﺑﻐ‬ ‫ﻮاء‬‫اﻟﮭ‬ ‫او‬ ‫ﺎﻟﻔﺮاغ‬ ‫ﺑ‬ ‫ﻌﺘﮭﺎ‬‫ﺳ‬ ‫ﻦ‬ ‫ﻋ‬
‫اﻻﺗﯿﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺔ‬ ‫ﻟﻠﻌﻼﻗﺔ‬ ‫وﻓﻘﺎ‬ ‫ﻋﻨﮫ‬ ‫ﻣﻨﻔﺼﻠﺔ‬:
‫ﻋﻨﻪ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫ام‬ ‫ﺑﺎﻟﻤﺼﺪر‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬
2-‫ﺰداد‬‫ﺗ‬ ‫ان‬ ‫ﺎ‬ ‫اﻣ‬ ‫ﻔﯿﺤﺘﯿﮭﺎ‬ ‫ﺻ‬ ‫ﻦ‬ ‫ﻣ‬ ‫أي‬ ‫ﻲ‬ ‫ﻓ‬ ‫ﺔ‬ ‫اﻟﻤﺨﺘﺰﻧ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬‫ﺴﺒﺔ‬ ‫ﺑﻨ‬)k()‫اذا‬‫ﺼﺪر‬ ‫ﺑﺎﻟﻤ‬ ‫ﺼﻠﺔ‬ ‫ﻣﺘ‬ ‫ﺴﻌﺔ‬ ‫اﻟﻤﺘ‬ ‫ﺖ‬‫ﻛﺎﻧ‬(‫ﻻ‬ ‫او‬‫ﺎﺛﺮ‬ ‫ﺗﺘ‬
)‫ﺛﺎﺑﺘﺔ‬ ‫ﺗﺒﻘﻰ‬(‫اﻻﺗﯿﺔ‬ ‫اﻟﻌﻼﻗﺎت‬ ‫ﻓﻲ‬ ‫ﻛﻤﺎ‬ ‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬:
CkCK =
‫ﻣﻼﺣﻈﺎت‬
Ck = k C
k
V
Vk
∆
=∆
k
E
EK =
C
C
k K
=

7. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-8-
‫ﺑﺎﻟﻤﺼﺪر‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬
or
‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬
‫اﻟﻌﺎزل‬ ‫ﻗﺒﻞ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺗﺴﺎوي‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ان‬ ‫أي‬.
3-‫ﺖ‬‫ﺛﺎﺑ‬ ‫ﻰ‬‫ﯾﺒﻘ‬ ‫ان‬ ‫ﺎ‬‫اﻣ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬)‫ﺼﺪر‬‫ﺑﺎﻟﻤ‬ ‫ﺼﻠﺔ‬‫ﻣﺘ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﺖ‬‫ﻛﺎﻧ‬ ‫اذا‬(‫ﻞ‬‫ﯾﻘ‬ ‫او‬‫ﺴﺒﺔ‬‫ﺑﻨ‬
)k(‫اﻟﮭﻮاء‬ ‫او‬ ‫ﺑﺎﻟﻔﺮاغ‬ ‫ﻗﯿﻤﺘﮫ‬ ‫ﻋﻦ‬)‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬(‫اﻟﺘﺎﻟﯿﺔ‬ ‫اﻟﻌﻼﻗﺎت‬ ‫ﻓﻲ‬ ‫ﻛﻤﺎ‬:
‫ﺑﺎﻟﻤﺼﺪر‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬
‫اﻟﻌﺎزل‬ ‫ﻗﺒﻞ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﯾﺴﺎوي‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ان‬ ‫أي‬.
or
‫اذا‬‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬
‫ﺖ‬‫ﻛﺎﻧ‬ ‫ﻮ‬ ‫ﻓﻠ‬ ‫ﺖ‬‫ﺛﺎﺑ‬ ‫ﻰ‬ ‫ﯾﺒﻘ‬ ‫ﺮ‬‫واﻻﺧ‬ ‫ﺮ‬‫ﯾﺘﻐﯿ‬ ‫ﺪھﻤﺎ‬ ‫ﻓﺎﺣ‬ ‫ﺪ‬ ‫واﺣ‬ ‫ان‬ ‫ﻲ‬‫ﻓ‬ ‫ﺮان‬‫ﯾﺘﻐﯿ‬ ‫ﻻ‬ ‫ﺪ‬ ‫اﻟﺠﮭ‬ ‫ﺮق‬‫وﻓ‬ ‫ﺸﺤﻨﺔ‬ ‫اﻟ‬ ‫ﺎن‬ ‫ﻓ‬ ‫ﺎزل‬‫اﻟﻌ‬ ‫ﻮد‬ ‫ﺑﻮﺟ‬ ‫ﺬﻟﻚ‬‫ﻟ‬
‫ا‬‫ﻣﺘﺼﻠﺔ‬ ‫ﻟﻤﺘﺴﻌﺔ‬‫ﺑﺎﻟﺒﻄﺎرﯾﺔ‬‫ﺗﺘﻐﯿﺮ‬)‫ﺗﺰداد‬(‫ﺼﻠﺔ‬‫ﻣﻨﻔ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﺖ‬‫ﻛﺎﻧ‬ ‫ﻮ‬‫وﻟ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫وﯾﺜﺒﺖ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻣﻊ‬ ‫طﺮدﯾﺔ‬ ‫ﺑﻌﻼﻗﺔ‬ ‫اﻟﺸﺤﻨﺔ‬
‫اﻟﺒﻄﺎرﯾﺔ‬ ‫ﻋﻦ‬‫ﯾﺘﻐﯿ‬‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺮ‬)‫ﯾﻘﻞ‬(‫اﻟﺸﺤﻨﺔ‬ ‫وﺗﺜﺒﺖ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻣﻊ‬ ‫ﻋﻜﺴﯿﺔ‬ ‫ﺑﻌﻼﻗﺔ‬.
4-‫ﺖ‬‫ﺛﺎﺑ‬ ‫ﻰ‬‫ﯾﺒﻘ‬ ‫ان‬ ‫ﺎ‬‫اﻣ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬)‫ﺼﺪر‬‫ﺑﺎﻟﻤ‬ ‫ﺼﻠﺔ‬‫ﻣﺘ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﺖ‬‫ﻛﺎﻧ‬ ‫اذا‬(‫ﺴﺒﺔ‬‫ﺑﻨ‬ ‫ﻞ‬‫ﯾﻘ‬ ‫او‬)k(
‫اﻟﮭﻮاء‬ ‫او‬ ‫ﺑﺎﻟﻔﺮاغ‬ ‫ﻗﯿﻤﺘﮫ‬ ‫ﻋﻦ‬)‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬(‫اﻟﺘﺎﻟﯿﺔ‬ ‫اﻟﻌﻼﻗﺎت‬ ‫ﻓﻲ‬ ‫ﻛﻤﺎ‬:
‫ﺑﺎﻟﻤﺼﺪر‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬
‫اﻟﻌﺎزل‬ ‫ﻗﺒﻞ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ﯾﺴﺎوي‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ان‬ ‫أي‬.
or
‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬
5-‫اﻣ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫اﻟﻤﺠﺎل‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬‫ﺰداد‬‫ﺗ‬ ‫ان‬ ‫ﺎ‬‫ﺴﺒﺔ‬‫ﺑﻨ‬(k)‫ﻮت‬‫وﺛﺒ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﺎدة‬‫زﯾ‬ ‫ﺴﺒﺐ‬‫ﺑ‬
‫ﺪ‬ ‫اﻟﺠﮭ‬ ‫ﺮق‬ ‫ﻓ‬)‫ﺼﺪر‬ ‫ﺑﺎﻟﻤ‬ ‫ﺼﻠﺔ‬ ‫ﻣﺘ‬ ‫ﺴﻌﺔ‬ ‫اﻟﻤﺘ‬ ‫ﺖ‬ ‫ﻛﺎﻧ‬ ‫اذا‬(‫ﺴﺒﺔ‬ ‫ﺑﻨ‬ ‫ﻞ‬ ‫ﺗﻘ‬ ‫او‬)k(‫ﺸﺤﻨﺔ‬ ‫اﻟ‬ ‫ﻮت‬ ‫وﺛﺒ‬ ‫ﺪ‬ ‫اﻟﺠﮭ‬ ‫ﺮق‬ ‫ﻓ‬ ‫ﺼﺎن‬ ‫ﻧﻘ‬ ‫ﺴﺒﺐ‬ ‫ﺑ‬
)‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬(‫اﻻﺗﯿﺔ‬ ‫اﻟﻌﻼﻗﺎت‬ ‫ﻓﻲ‬ ‫وﻛﻤﺎ‬.
‫اﻟ‬ ‫ﻟﻠﻤﺘﺴﻌﺔ‬‫ﺑﺎﻟﻤﺼﺪر‬ ‫ﻤﺘﺼﻠﺔ‬
or
‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫اﻟﻤﻨﻔﺼﻠﺔ‬ ‫ﻟﻠﻤﺘﺴﻌﺔ‬
k
PE
PEk =
PEkPEk =
k
E
Ek =
EEK =
k
V
Vk
∆
=∆
VVK ∆=∆
QQK =
QkQK =

8. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-9-
‫اﻟﻤﺘﻮازﯾﺘﯿﻦ‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ذات‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬ ‫ﻋﻠﯿﮭﺎ‬ ‫ﺗﻌﺘﻤﺪ‬ ‫اﻟﺘﻲ‬ ‫اﻟﻌﻮاﻣﻞ‬:
1-‫اﻟﺴﻄﺤﯿﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬)A(‫ﺼﻔﯿﺤﺘﯿﻦ‬‫اﻟ‬ ‫ﻦ‬‫ﻣ‬ ‫ﻞ‬‫ﻟﻜ‬ ‫اﻟﻤﺘﻘﺎﺑﻠﺔ‬:‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻌﺔ‬‫ﺳ‬ ‫ﺐ‬‫ﺗﺘﻨﺎﺳ‬ ‫ﺚ‬‫ﺣﯿ‬)C(‫ﺴﺎﺣﺔ‬‫اﻟﻤ‬ ‫ﻊ‬‫ﻣ‬ ‫ﺎ‬‫طﺮدﯾ‬ ‫ﺒﺎ‬‫ﺗﻨﺎﺳ‬
‫اﻟﺴﻄﺤ‬‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﻣﻦ‬ ‫ﻟﻜﻞ‬ ‫اﻟﻤﺘﻘﺎﺑﻠﺔ‬ ‫ﯿﺔ‬‫اﻟﺒﻌﺪ‬ ‫ﺑﺜﺒﻮت‬)d(‫و‬‫اﻟﻮﺳﻂ‬‫اﻟﻌﺎزل‬.‫ان‬ ‫أي‬:)AC( α
2-‫اﻟﺒﻌﺪ‬)d(‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬.‫ﻋﻜﺴﯿﺎ‬ ‫ﻣﻌﮫ‬ ‫وﺗﺘﻨﺎﺳﺐ‬‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﺑﺜﺒﻮت‬)A(‫اﻟﻌﺎزل‬ ‫واﻟﻮﺳﻂ‬.‫ان‬ ‫أي‬:)
d
1
C( α.
3-‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻌﺎزل‬ ‫اﻟﻮﺳﻂ‬ ‫ﻧﻮع‬:‫ﺗ‬ ‫ﺣﯿﺚ‬‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬ ‫ﺰداد‬‫ﺑﺈدﺧﺎل‬‫ﻋﺎزﻟﺔ‬ ‫ﻣﺎدة‬‫ﺎ‬‫ﻛﮭﺮﺑﺎﺋﯿ‬‫ﻦ‬‫ﻣ‬ ‫ﺪﻻ‬‫ﺑ‬ ‫ﺼﻔﯿﺤﺘﯿﻦ‬‫اﻟ‬ ‫ﯿﻦ‬‫ﺑ‬
‫اﻟﮭﻮاء‬‫أو‬‫اﻟﻔﺮاغ‬‫اﻟﺴﻄﺤﯿﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﺑﺜﺒﻮت‬)A(‫واﻟﺒﻌﺪ‬)d.(‫ﺣﯿﺚ‬:Ck = K C
‫اﻟﻌ‬ ‫ﯾﻜﻮن‬ ‫وﻋﻨﺪﻣﺎ‬‫ﺎ‬‫اﻟﺒﻌﺪ‬ ‫ﻣﻊ‬ ‫وﻋﻜﺴﯿﺎ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﻣﻊ‬ ‫طﺮدﯾﺎ‬ ‫ﺗﺘﻨﺎﺳﺐ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻓﺎن‬ ‫ھﻮاء‬ ‫او‬ ‫ﻓﺮاغ‬ ‫زل‬)
d
A
Cα(‫ﻟﺬﻟﻚ‬‫ﻓﺎ‬‫ن‬:
‫ﺣﯿﺚ‬:
ο
ε:‫وﯾﺴﻤﻰ‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫ﻋﺎزﻻ‬ ‫اﻟﮭﻮاء‬ ‫او‬ ‫اﻟﻔﺮاغ‬ ‫ﻛﺎن‬ ‫اذا‬ ‫اﻟﺘﻨﺎﺳﺐ‬ ‫ﺛﺎﺑﺖ‬‫اﻟﻔﺮاغ‬ ‫ﺳﻤﺎﺣﯿﺔ‬‫وﻣﻘﺪارھﺎ‬
)8.85×10 – 12
C2
/ N . m2
=ºЄ(
C:‫اﻟﻔﺎراد‬ ‫ﺑﻮﺣﺪة‬)F(،d:‫ﻣﺘﺮ‬ ‫ﺑﻮﺣﺪة‬)m(،A:‫ﺑﻮﺣﺪة‬)m2
. (
‫ﻛﺬﻟﻚ‬:
‫ﺣﯿﺚ‬:
Ck:‫ﻋﺎزﻟﺔ‬ ‫ﻣﺎدة‬ ‫ﺑﻮﺟﻮد‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬.‫ﻧﺠﺪ‬ ‫اﻋﻼه‬ ‫اﻟﻌﻼﻗﺎت‬ ‫ﻣﻦ‬:
♦‫ان‬ ‫ﻧﺠﺪ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬ ‫ﻋﻠﯿﮫﺎ‬ ‫ﺗﻌﺘﻤﺪ‬ ‫اﻟﺘﻲ‬ ‫اﻟﻌﻮاﻣﻞ‬ ‫ﻣﻦ‬:
2
1
1
2
d
d
C
C
d
1
C =⇒αQ
1
2
1
2
A
A
C
C
AC =⇒αQ
d
A
C οε=
d
A
kCk
οε
=
CK=k C
‫ﺖ‬‫ﺛﺎﺑ‬ ‫ﻮاء‬‫اﻟﮭ‬ ‫او‬ ‫ﺮاغ‬‫اﻟﻔ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺑﺪﻻ‬ ‫ﻛﮭﺮﺑﺎﺋﯿﺎ‬ ‫ﻋﺎزﻟﺔ‬ ‫ﻣﺎدة‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫ﯾﻔﺼﻞ‬ ‫ﻋﻨﺪﻣﺎ‬
‫ﻋﺰﻟﮭﺎ‬K.
‫اﻟﮭﻮاء‬ ‫او‬ ‫اﻟﻔﺮاغ‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫ﯾﻔﺼﻞ‬ ‫ﻋﻨﺪﻣﺎ‬
‫اﻟﺒﻌﺪ‬ ‫ﺑﺜﺒﻮت‬‫ھﻮاء‬ ‫او‬ ‫ﻓﺮاغ‬ ‫واﻟﻌﺎزل‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬
‫ﺑﺜﺒﻮت‬‫ھﻮاء‬ ‫او‬ ‫ﻓﺮاغ‬ ‫واﻟﻌﺎزل‬ ‫اﻟﻤﺘﻘﺎﺑﻠﺔ‬ ‫اﻟﺴﻄﺤﯿﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬

9. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-10-
‫س‬/‫ﺼﻔﯿﺤﺘﻲ‬ ‫ﻟ‬ ‫ﺔ‬ ‫اﻟﻤﺘﻘﺎﺑﻠ‬ ‫ﺴﻄﺤﺔ‬ ‫اﻟ‬ ‫ﺴﺎﺣﺔ‬ ‫اﻟﻤ‬ ‫ﻌﻒ‬ ‫ﺿ‬ ‫ﺪاھﻤﺎ‬ ‫اﺣ‬ ‫ﺼﻔﯿﺤﺘﻲ‬ ‫ﻟ‬ ‫ﺔ‬ ‫اﻟﻤﺘﻘﺎﺑﻠ‬ ‫ﺴﻄﺤﯿﺔ‬ ‫اﻟ‬ ‫ﺴﺎﺣﺔ‬ ‫اﻟﻤ‬ ‫ﺴﻌﺘﺎن‬ ‫ﻣﺘ‬ ‫ﺪﯾﻚ‬ ‫ﻟ‬
‫ھﻮاء؟‬ ‫او‬ ‫ﻓﺮاغ‬ ‫اﻟﻌﺎزل‬ ‫ﻛﺎن‬ ‫اذا‬ ‫ﺳﻌﺘﯿﮭﺎ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻨﺴﺒﺔ‬ ‫ﻣﺎ‬ ‫اﻻﺧﺮى‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺒﻌﺪ‬ ‫ﻧﺼﻒ‬ ‫ﺻﻔﯿﺤﺘﯿﮭﺎ‬ ‫ﺑﯿﻦ‬ ‫واﻟﺒﻌﺪ‬ ‫اﻻﺧﺮى‬
‫ج‬/
4
C
C
d
2
1
A
dA2
C
C
d
2
1
d,A2A,
dA
dA
C
C
d
A
d
A
C
C
2
1
22
22
2
1
2121
12
21
2
1
2
2
1
1
2
1
=⇒
×
=∴
===⇒
ε
ε
=
ο
ο
Q
‫ﻣﻼﺣﻈﺎﺕ‬/
1-‫اﻟﻌﻼﻗﺔ‬ ‫ﻣﻦ‬‫اﻟﺘﺎﻟﯿﺔ‬:
V
Q
C
∆
=‫أن‬ ‫ﻧﺠﺪ‬:
a(‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻌﺔ‬‫ﺳ‬ ‫ﻊ‬‫ﻣ‬ ‫ﺎ‬‫طﺮدﯾ‬ ‫ﺐ‬‫ﺗﺘﻨﺎﺳ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﻣﻦ‬ ‫اي‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﺸﺤﻨﺔ‬)‫ﺪ‬‫اﺣ‬ ‫ﺮ‬‫ﺑﺘﻐﯿ‬ ‫ﺴﻌﺔ‬‫اﻟ‬ ‫ﺮت‬‫ﺗﻐﯿ‬ ‫ﻮ‬‫ﻟ‬ ‫ﺎ‬‫ﻓﯿﻤ‬
‫ﻋﻮاﻣﻠﮭﺎ‬(‫ﺑﯿﻨﮭﻤﺎ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬)‫ﺗﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﯾﺜﺒﺖ‬ ‫ﺣﯿﺚ‬‫ﺑﺎﻟﺒﻄﺎرﯾﺔ‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬(
‫ان‬ ‫أي‬:CQα)‫ﺑﺜﺒﻮت‬∆V(
b(‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻌﺔ‬‫ﺳ‬ ‫ﻊ‬‫ﻣ‬ ‫ﺴﯿﺎ‬‫ﻋﻜ‬ ‫ﺐ‬‫ﯾﺘﻨﺎﺳ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫ﻓ‬)‫ﺪ‬‫اﺣ‬ ‫ﺮ‬‫ﺑﺘﻐﯿ‬ ‫ﺴﻌﺔ‬‫اﻟ‬ ‫ﺮت‬‫ﺗﻐﯿ‬ ‫ﻮ‬‫ﻟ‬ ‫ﺎ‬‫ﻓﯿﻤ‬
‫ﻋﻮاﻣﻠﮭﺎ‬(‫ﺷﺤﻨﺘﮭﺎ‬ ‫ﺛﺒﻮت‬ ‫ﻋﻨﺪ‬)‫اﻟﺒﻄﺎرﯾﺔ‬ ‫ﻋﻦ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺗﻔﺼﻞ‬ ‫ﻋﻨﺪﻣﺎ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺗﺜﺒﺖ‬ ‫ﺣﯿﺚ‬(‫ان‬ ‫أي‬:
C
1
V α∆)‫ﺑﺜﺒﻮت‬Q.(
c(‫ﺗﺘﻐﯿﺮ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬ ‫ﺑﺎن‬ ‫ﺗﺬﻛﺮ‬‫ﻋﻠﯿﮭﺎ‬ ‫اﻟﻤﺆﺛﺮ‬ ‫اﻟﻌﻮاﻣﻞ‬ ‫اﺣﺪ‬ ‫ﺑﺘﻐﯿﺮ‬)‫ﯿﻦ‬‫ﺑ‬ ‫اﻟﺒﻌﺪ‬ ‫او‬ ‫اﻟﻤﺘﻮازﯾﺘﯿﻦ‬ ‫ﻟﻠﺼﻔﯿﺤﺘﯿﻦ‬ ‫اﻟﻤﺘﻘﺎﺑﻠﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬
‫اﻟﻔﺮاغ‬ ‫او‬ ‫اﻟﮭﻮاء‬ ‫ﻣﻦ‬ ‫ﺑﺪﻻ‬ ‫ﺻﻔﯿﺤﺘﯿﮭﺎ‬ ‫ﺑﯿﻦ‬ ‫ﻋﺎزﻟﺔ‬ ‫ﻣﺎدة‬ ‫إدﺧﺎل‬ ‫او‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬. (
d(‫اﻟﻜﮭﺮﺑﺎﺋ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬‫ﺪ‬‫ﻋﻨ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﻦ‬‫ﻣ‬ ‫أي‬ ‫ﻲ‬‫ﻓ‬ ‫ﺔ‬‫اﻟﻤﺨﺘﺰﻧ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﻣﻊ‬ ‫طﺮدﯾﺎ‬ ‫ﯾﺘﻨﺎﺳﺐ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫ﻲ‬
‫اﻟﺴﻌﺔ‬ ‫ﺛﺒﻮت‬.‫ان‬ ‫أي‬
∆V α Q)‫ﺑﺜﺒﻮت‬(C
2-‫واﺣﺪ‬ ‫ﻣﻦ‬ ‫اﻛﺒﺮ‬ ‫داﺋﻤﺎ‬ ‫ﯾﻜﻮن‬ ‫اﻻﺧﺮى‬ ‫اﻟﻌﺎزﻟﺔ‬ ‫ﻟﻠﻤﻮاد‬ ‫ﺑﯿﻨﻤﺎ‬ ‫واﺣﺪ‬ ‫ﯾﺴﺎوي‬ ‫اﻟﮭﻮاء‬ ‫او‬ ‫ﻟﻠﻔﺮاغ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻌﺰل‬ ‫ﺛﺎﺑﺖ‬.
3-‫ﺑﺸﺤﻨﺔ‬ ‫اﻟﻤﻘﺼﻮد‬‫ﺻﻔﯿﺤﺘﯿﮭﺎ‬ ‫ﻣﻦ‬ ‫أي‬ ‫ﺷﺤﻨﺔ‬ ‫ھﻲ‬ ‫اﻟﻤﺘﺴﻌﺔ‬)‫اﻟﺴﺎﻟﺒﺔ‬ ‫او‬ ‫اﻟﻤﻮﺟﺒﺔ‬(‫اﻟﻜﻠﯿﺔ‬ ‫ﺷﺤﻨﺘﮭﺎ‬ ‫وﻟﯿﺲ‬.
4-‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺒﻌﺪ‬ ‫ﯾﺴﺎوي‬ ‫ﺳﻤﻜﮫ‬ ‫ﻓﺎن‬ ‫ﺗﻤﺎﻣﺎ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺤﯿﺰ‬ ‫اﻟﻌﺎزل‬ ‫ﯾﻤﻸ‬ ‫ﻋﻨﺪﻣﺎ‬.
‫اﻟﻤﻨﻔﺮدة‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻗﻮاﻧﻴﻦ‬ ‫ﺧﻼﺻﺔ‬:
‫اﻟﻌﺎزل‬ ‫ﻗﺒﻞ‬:
,
‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬:
,
d
V
E k
k
∆
=d
A
kCor
V
Q
C k
k
k
k οε=
∆
=
C
Q
.
2
1
PEor)V.(C
2
1
PEorQ.V
2
1
PE
2
2
=∆=∆=
d
V
E
∆
=
d
A
Cor
V
Q
C οε=
∆
=

10. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-11-
+ -
∆Vtotal
C1
C2
n21total V.........VVV ∆=∆=∆=∆
n21total Q.........QQQ ++=
n21eq C.........CCC ++=
‫اﻟﻌﻼﻗﺎت‬:
‫ﺑﺎﻟﻤﺼﺪر‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬‫اﻟﻤﺼﺪ‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬‫ر‬
CkCk =CkCk =
QkQk =QQk =
VVk ∆=∆
k
V
Vk
∆
=∆
EEk =
k
E
Ek =
PEkPEk =
k
PE
PEk =
‫ﺍﳌ‬ ‫ﺭﺑﻂ‬‫ﺘﺴﻌﺎﺕ‬)‫ﺗﻮﺍﱄ‬ ، ‫ﺗﻮﺍﺯﻱ‬(:
‫أوﻻ‬:‫اﻟﺘﻮازي‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫رﺑﻂ‬:
‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬‫رﺑﻂ‬n‫ﻓﺎن‬ ‫اﻟﺘﻮازي‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬:
`1-‫ﺴﻌﺎت‬‫اﻟﻤﺘ‬ ‫ﻊ‬‫ﺟﻤﯿ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﺴﺎوي‬‫ﻣﺘ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﻓﺮق‬)‫ﺖ‬‫ﺛﺎﺑ‬(‫ﺪ‬‫ﺟﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﺴﺎوي‬‫وﯾ‬
‫اﻟﺒﻄﺎرﯾﺔ‬)‫اﻟﻜﻠﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬(‫ان‬ ‫أي‬:
2-‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻋﻠﻰ‬ ‫اﻟﺸﺤﻨﺎت‬ ‫ﻣﺠﻤﻮع‬ ‫ﺗﺴﺎوي‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬)‫ﺗﺘﻮزع‬(‫ان‬ ‫أي‬:
3-‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬)Ceq(‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﺳﻌﺎت‬ ‫ﻣﺠﻤﻮع‬ ‫ﺗﺴﺎوي‬‫اﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﻓﻲ‬ ‫ﺳﻌﺔ‬ ‫اﻛﺒﺮ‬ ‫ﻣﻦ‬ ‫اﻛﺒﺮ‬ ‫وﺗﻜﻮن‬‫ان‬ ‫أي‬:
4-‫ﺔ‬‫ﻣﺘﻤﺎﺛﻠ‬ ‫ﺴﻌﺎت‬‫ﻣﺘ‬ ‫ﻟﻤﺠﻤﻮﻋﺔ‬ ‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬)‫اي‬‫ﺴﻌﺔ‬‫اﻟ‬ ‫ﺴﺎوﯾﺔ‬‫ﻣﺘ‬(‫ﺴﻌﺎت‬‫اﻟﻤﺘ‬ ‫ﺪد‬‫ﻋ‬ ‫ﺴﺎوي‬‫ﺗ‬)n(‫ﺎ‬‫ﻣﻨﮭ‬ ‫ﺪة‬‫واﺣ‬ ‫ﻌﺔ‬‫ﺳ‬ ‫ﻲ‬‫ﻓ‬.
‫ان‬ ‫أي‬:
5-‫ﺔ‬‫اﻟﻄﺎﻗ‬ ‫ﻮع‬‫ﻣﺠﻤ‬ ‫ﺴﺎوي‬‫ﺗ‬ ‫ﻮازي‬‫اﻟﺘ‬ ‫ﺔ‬‫ﻟﻤﺠﻤﻮﻋ‬ ‫ﺔ‬‫اﻟﻤﻜﺎﻓﺌ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬‫اﻟﻤﺠ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺔ‬‫اﻟﻤﺨﺘﺰﻧ‬ ‫ﺔ‬‫اﻟﻄﺎﻗ‬
‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻛﻞ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬.‫ان‬ ‫أي‬:
n21T PE.........PEPEPE ++=
CnCeq =
k
2
k
k
2
kkkkkk
C
Q
.
2
1
PEor)V.(C
2
1
PEorQ.V
2
1
PE =∆=∆=
‫ﻣﺮ‬ ‫ﻣﺘﺴﻌﺎت‬ ‫ﻟﻤﺠﻤﻮﻋﺔ‬ ‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻹﯾﺠﺎد‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ھﺬه‬ ‫ﺗﺴﺘﺨﺪم‬‫اﻟﺘﻮازي‬ ‫ﻋﻠﻰ‬ ‫ﺑﻮطﺔ‬

11. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-12-
+ -
C1 C2
∆Vtotal
n21total V.........VVV ∆+∆+∆=∆
n21total Q.........QQQ ===
‫س‬/‫اﻟﺴﻌﺔ‬ ‫ﻟﺤﺴﺎب‬ ‫ﻋﻼﻗﺔ‬ ‫اﺷﺘﻖ‬‫اﻟﻤﻜﺎﻓﺌﺔ‬)Ceq(‫ﻟ‬‫ﻤ‬‫اﻟﺘﻮازي‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺮﺑﻮطﺔ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﺠﻤﻮﻋﺔ‬.
‫ج‬/
21eq21eq21eq
21total
2211totaleq21total
CCCV).CC(V.CV.CV.CV.C
VVVV
V.CV.CV.CQQQ
+=⇒∆+=∆⇒∆+∆=∆∴
∆=∆=∆=∆
∆+∆=∆⇒+=
Q
‫ﺗﻨﻮﯾﮫ‬/
‫ﻮازي‬‫اﻟﺘ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﺴﻌﺘﯿﻦ‬‫ﻣﺘ‬ ‫ﻂ‬‫رﺑ‬ ‫ﺪ‬‫ﻋﻨ‬)‫ﺼﺪر‬ ‫ﻣ‬ ‫ﺪون‬‫ﺑ‬(‫ﺴﻌﺘﯿﻦ‬‫اﻟﻤﺘ‬ ‫ﻮن‬‫ﺗﻜ‬ ‫ان‬ ‫ﻰ‬‫ﻋﻠ‬‫ﺪ‬ ‫ﺟﮭ‬ ‫ﺮق‬‫ﻟﻔ‬ ‫ﺴﺒﻘﺎ‬‫ﻣ‬ ‫ﺸﺤﻮﻧﺘﯿﻦ‬‫ﻣ‬
‫ﻣﺸﺤﻮﻧﺔ‬ ‫ﻏﯿﺮ‬ ‫واﻻﺧﺮى‬ ‫ﻣﺸﺤﻮﻧﺔ‬ ‫اﺣﺪاھﻤﺎ‬ ‫او‬ ‫ﻣﺨﺘﻠﻒ‬‫اﻟﺘﺎﻟﻲ‬ ‫ﺑﺎﻟﺸﻜﻞ‬ ‫ﺗﻜﻮن‬ ‫اﻟﺤﻞ‬ ‫ﺧﻄﻮات‬ ‫ﻓﺎن‬:
1-‫ﻟﻢ‬ ‫ان‬ ‫اﻟﺘﻮﺻﯿﻞ‬ ‫ﻗﺒﻞ‬ ‫اﻟﻤﺘﺴﻌﺘﯿﻦ‬ ‫ﻣﻦ‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﻛﻞ‬ ‫ﺷﺤﻨﺔ‬ ‫ﻧﺠﺪ‬‫اﻟﻘﺎﻧﻮن‬ ‫ﻣﻦ‬ ‫ﻣﻮﺟﻮدة‬ ‫ﺗﻜﻦ‬:
222
111
V.CQ
V.CQ
∆=
∆=
2-‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻟﻠﺤﺼﻮل‬ ‫اﻟﺘﻮازي‬ ‫ﺧﻮاص‬ ‫ﻣﻦ‬ ‫اﻟﻤﺘﺴﻌﺘﯿﻦ‬ ‫ﺷﺤﻨﺔ‬ ‫ﻧﺠﻤﻊ‬:
21T QQQ +=
3-‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻟﻠﺤﺼﻮل‬ ‫اﻟﻤﺘﺴﻌﺘﯿﻦ‬ ‫ﺳﻌﺔ‬ ‫ﻧﺠﻤﻊ‬:
21eq CCC +=
4-‫ﯾ‬ ‫واﻟﺬي‬ ‫ﻟﻠﻤﺘﺴﻌﺘﯿﻦ‬ ‫اﻟﻜﻠﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻧﺴﺘﺨﺮج‬‫ﺗﻮازي‬ ‫اﻟﺮﺑﻂ‬ ‫ﻟﻜﻮن‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﻛﻞ‬ ‫ﺟﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺴﺎوي‬:
21
eq
T
T VV
C
Q
V ∆=∆==∆
5-‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫ﺑﺎﻟﻘﺎﻧﻮن‬ ‫اﻟﻤﺘﺴﻌﺘﯿﻦ‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺗﻮزﯾﻊ‬ ‫ﻧﻌﯿﺪ‬:
222
111
V.CQ
V.CQ
∆=
∆=
v‫اﻟﺘﻮﺻﯿﻞ‬ ‫ﺑﻌﺪ‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺗﺴﺎوي‬ ‫اﻟﺘﻮﺻﯿﻞ‬ ‫ﻗﺒﻞ‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺗﻜﻮن‬ ‫ان‬ ‫ﯾﺠﺐ‬ ‫اﻟﺤﻞ‬ ‫ﺻﺤﺔ‬ ‫ﻣﻦ‬ ‫ﻟﻠﺘﺎﻛﺪ‬.
v‫ھﺬه‬‫ﺑﻌﺾ‬ ‫ﻣﻊ‬ ‫اﻟﻤﺘﻤﺎﺛﻠﺔ‬ ‫اﻟﺼﻔﺎﺋﺢ‬ ‫رﺑﻂ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬ ‫ﺗﺴﺘﺨﺪم‬ ‫اﻟﺨﻄﻮات‬)‫ﺔ‬‫ﻟﻠﻤﻮﺟﺒ‬ ‫اﻟﻤﻮﺟﺒﺔ‬ ‫اﻟﺼﻔﯿﺤﺔ‬ ‫أي‬‫ﺴﺎﻟﺒﺔ‬‫اﻟ‬ ‫ﺼﻔﯿﺤﺔ‬‫واﻟ‬
‫ﻟﻠﺴﺎﻟﺒﺔ‬. (
v‫ﺔ‬‫اﻟﺜﺎﻧﯿ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻦ‬‫ﻣ‬ ‫ﻔﯿﺤﺔ‬‫ﺻ‬ ‫ﻛﻞ‬ ‫ﺷﺤﻨﺔ‬ ‫ﻣﻊ‬ ‫اﻻوﻟﻰ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻣﻦ‬ ‫ﺻﻔﯿﺤﺔ‬ ‫ﻛﻞ‬ ‫ﺷﺤﻨﺔ‬ ‫ﻓﺘﺘﻌﺎدل‬ ‫اﻟﻤﺨﺘﻠﻔﺔ‬ ‫اﻟﺼﻔﺎﺋﺢ‬ ‫رﺑﻂ‬ ‫ﻋﻨﺪ‬
‫ﺗﺴﺎ‬ ‫اﻟﺘﻮﺻﯿﻞ‬ ‫ﺑﻌﺪ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﻛﻞ‬ ‫ﺷﺤﻨﺔ‬ ‫وﺗﺼﺒﺢ‬‫ﺻﻔﺮ‬ ‫وي‬‫ﻮ‬‫ﻟ‬ ‫ﺎ‬‫اﻣ‬ ‫ﺴﺎوﯾﺔ‬‫ﻣﺘ‬ ‫ﺴﻌﺘﯿﻦ‬‫اﻟﻤﺘ‬ ‫ﺤﻨﺔ‬‫ﺷ‬ ‫ﺖ‬‫ﻛﺎﻧ‬ ‫ﻮ‬‫ﻟ‬ ‫ﺎ‬‫ﻓﯿﻤ‬
‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﺼﻮل‬‫ﻟﻠﺤ‬ ‫ﺴﻌﺘﯿﻦ‬‫اﻟﻤﺘ‬ ‫ﺤﻨﺔ‬‫ﺷ‬ ‫ﻧﺠﻤﻊ‬ ‫ان‬ ‫ﻣﻦ‬ ‫وﺑﺪﻻ‬ ‫اﻋﻼه‬ ‫اﻟﻘﻮاﻋﺪ‬ ‫ﻧﻔﺲ‬ ‫ﻓﻨﺘﺒﻊ‬ ‫ﻣﺨﺘﻠﻔﺔ‬ ‫اﻟﻤﺘﺴﻌﺘﯿﻦ‬ ‫ﺷﺤﻨﺔ‬ ‫ﻛﺎﻧﺖ‬
‫ﻧﻄﺮﺣﮭﻤﺎ‬ ‫اﻟﻜﻠﯿﺔ‬.
‫ﺛﺎﻧﯿﺎ‬:‫اﻟﺘﻮاﻟﻲ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫رﺑﻂ‬:
‫رﺑﻂ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬n‫ﻓﺎن‬ ‫اﻟﺘﻮاﻟﻲ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬:
1-‫ﻣﻘﺪار‬‫اﻟ‬ ‫ﺟﻤﯿﻊ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺘﺴﺎوي‬ ‫اﻟﺸﺤﻨﺔ‬‫ان‬ ‫أي‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫وﯾﺴﺎوي‬ ‫ﻤﺘﺴﻌﺎت‬:
2-‫اﻟﻜﻠﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬)∆Vtotal(‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻋﻠﻰ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮوق‬ ‫ﻣﺠﻤﻮع‬ ‫ﯾﺴﺎوي‬)‫ﯾﺘﻮزع‬(‫ان‬ ‫أي‬:

12. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-13-
n21eq C
1
.........
C
1
C
1
C
1
++=
3-‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻣﻘﻠﻮب‬‫ﻟﻠﻤﺠﻤﻮﻋﺔ‬‫ﯾﺴﺎوي‬‫ﺳﻌﺎت‬ ‫ﻣﻘﻠﻮب‬ ‫ﻣﺠﻤﻮع‬‫ﺔ‬‫اﻟﻤﻜﺎﻓﺌ‬ ‫ﺴﻌﺔ‬‫اﻟ‬ ‫ﺪار‬‫ﻣﻘ‬ ‫ﺎن‬‫ﻓ‬ ‫وﺑﺎﻟﺘﺎﻟﻲ‬ ‫اﻟﻤﺘﺴﻌﺎت‬)Ceq(
‫اﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﻓﻲ‬ ‫ﺳﻌﺔ‬ ‫اﺻﻐﺮ‬ ‫ﻣﻦ‬ ‫اﺻﻐﺮ‬ ‫وﯾﻜﻮن‬ ‫ﯾﻘﻞ‬‫ان‬ ‫أي‬:
♦‫ﻓﻲ‬‫اﻟﻤﻜﺎﻓﺌـﺔ‬ ‫اﻟـﺴﻌﺔ‬ ‫ﻧﺤـﺴﺐ‬ ‫أن‬ ‫ﻳﻤﻜـﻦ‬ ‫اﻟﺘﻮاﻟﻲ‬ ‫ﻋﻠﻰ‬ ‫ﻓﻘﻂ‬ ‫ﻣﺘﺴﻌﺘﻴﻦ‬ ‫رﺑﻂ‬ ‫ﺣﺎﻟﺔ‬‫ﻟﻬﻤـﺎ‬‫ﻣـﻦ‬‫اﻟـﺴﻌﺘﻴﻦ‬ ‫ﺿـﺮب‬ ‫ﺣﺎﺻـﻞ‬
‫اﻟﺴﻌﺘﻴﻦ‬ ‫ﻣﺠﻤﻮع‬ ‫ﻋﻠﻰ‬‫وﻓﻘﺎ‬‫ﻟ‬‫اﻻ‬ ‫ﻠﻌﻼﻗﺔ‬‫ﺗﻴﺔ‬:
4-‫ﻟﻤﺠﻤﻮ‬ ‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬‫ﻣﺘﻤﺎﺛﻠﺔ‬ ‫ﻣﺘﺴﻌﺎت‬ ‫ﻋﺔ‬)‫اﻟﺴﻌﺔ‬ ‫ﻣﺘﺴﺎوﯾﺔ‬ ‫اي‬(‫ﺴﻌﺎت‬‫اﻟﻤﺘ‬ ‫ﺪد‬‫ﻋ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬ ‫واﺣﺪ‬ ‫ﺳﻌﺔ‬ ‫ﺗﺴﺎوي‬
)n. (‫ان‬ ‫أي‬:
5-‫اﻟﻄ‬ ‫ﻮع‬ ‫ﻣﺠﻤ‬ ‫ﺴﺎوي‬‫ﺗ‬ ‫ﻮاﻟﻲ‬ ‫اﻟﺘ‬ ‫ﺔ‬ ‫ﻟﻤﺠﻤﻮﻋ‬ ‫ﺔ‬‫اﻟﻤﻜﺎﻓﺌ‬ ‫ﺴﻌﺔ‬ ‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬ ‫اﻟﻤﺠ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺔ‬ ‫اﻟﻤﺨﺘﺰﻧ‬ ‫ﺔ‬‫اﻟﻄﺎﻗ‬‫ﺔ‬ ‫ﺎﻗ‬
‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻛﻞ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬.‫ان‬ ‫أي‬:
‫س‬/‫اﺷﺘﻖ‬‫ﻟﺤﺴﺎب‬ ‫ﻋﻼﻗﺔ‬‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬)Ceq(‫ﻟ‬‫ﻤ‬‫ﺠﻤﻮﻋﺔ‬‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬‫اﻟﺘﻮاﻟﻲ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺮﺑﻮطﺔ‬.
‫ج‬/
21eq21eq21eq
21total
2
2
1
1
eq
total
21total
C
1
C
1
C
1
)
C
1
C
1
.(Q
C
Q
C
Q
C
Q
C
Q
QQQQ
C
Q
C
Q
C
Q
VVV
+=⇒+=⇒+=∴
===
+=⇒∆+∆=∆
Q
‫ﺛﺎﻟﺜﺎ‬:‫اﻟﻤﺨﺘﻠﻂ‬ ‫اﻟﺮﺑﻂ‬:
♦‫واﻟﺘﻮاﻟﻲ‬ ‫اﻟﺘﻮازي‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫رﺑﻂ‬ ‫ﻋﻨﺪ‬)‫رﺑﻂ‬‫ﻣﺨﺘﻠﻂ‬(‫ﻣﻌـﺎ‬ ‫واﻟﺘﻮاﻟﻲ‬ ‫اﻟﺘﻮازي‬ ‫ﺧﻮاص‬ ‫ﺗﻄﺒﻴﻖ‬ ‫ﻓﻴﺠﺐ‬‫ﻓﻠـﻮ‬
‫اﻟﺘ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺘﺴﻌﺘﺎن‬ ‫ﻣﺜﻼ‬ ‫ﻛﺎﻧﺖ‬‫ﻣﻜﺎﻓﺌـﺔ‬ ‫ﻣﺘـﺴﻌﺔ‬ ‫اوﻻ‬ ‫ﻧـﺴﺘﺨﺮج‬ ‫اﻟﺘـﻮاﻟﻲ‬ ‫ﻋﻠـﻰ‬ ‫ﺛﺎﻟﺜﺔ‬ ‫وﻣﻊ‬ ‫ﻮازي‬‫ﻟ‬‫اﻟ‬ ‫ﻤﺠﻤﻮﻋـﺔ‬‫ﺘـﻮازي‬‫ﻓﻴﺘﺤـﻮل‬
‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻧﺠﺪ‬ ‫ﺛﻢ‬ ‫ﺗﻮاﻟﻲ‬ ‫اﻟﻰ‬ ‫اﻟﺮﺑﻂ‬)‫ﺑﺎﻟﻤﻘﻠﻮب‬.(‫ﻣـﻊ‬ ‫اﻟﺘﻮاﻟﻲ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺘﺴﻌﺘﺎن‬ ‫ﻣﺜﻼ‬ ‫ﻛﺎﻧﺖ‬ ‫وﻟﻮ‬‫اﻟﺘـﻮازي‬ ‫ﻋﻠـﻰ‬ ‫ﺛﺎﻟﺜـﺔ‬
‫ﻧﺴ‬‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬ ‫اوﻻ‬ ‫ﺘﺨﺮج‬‫ﻟ‬‫اﻟ‬ ‫ﻤﺠﻤﻮﻋﺔ‬‫ﺘﻮاﻟﻲ‬‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻧﺠﺪ‬ ‫ﺛﻢ‬ ‫ﺗﻮازي‬ ‫اﻟﻰ‬ ‫اﻟﺮﺑﻂ‬ ‫ﻓﻴﺘﺤﻮل‬)‫ﺑﺎﻟﻤﺠﻤﻮع‬.(
♦‫ﻣﺮﺑﻮﻃﺔ‬ ‫ﻣﺘﺴﻌﺎت‬ ‫ﻟﻤﺠﻤﻮﻋﺔ‬ ‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬ ‫ﺗﻜﻮن‬‫ﻣﺨﺘﻠﻂ‬ ‫رﺑﻂ‬ ‫او‬ ‫ﺗﻮاﻟﻲ‬ ‫رﺑﻂ‬)‫ﺗﻮازي‬‫و‬‫ﺗﻮاﻟﻲ‬(‫اﻟـﺴﻌﺔ‬ ‫ﻣﻦ‬ ‫اﺻﻐﺮ‬ ‫ﻫﻲ‬
‫ﺗﻮازي‬ ‫رﺑﻂ‬ ‫ﻣﺮﺑﻮﻃﺔ‬ ‫ﻣﺘﺴﻌﺎت‬ ‫ﻟﻤﺠﻤﻮﻋﺔ‬ ‫اﻟﻤﻜﺎﻓﺌﺔ‬.
n21T PE.........PEPEPE ++=
n
C
Ceq =
21
21
eq
CC
C.C
C
+
=
‫اﻟﻤﻜﺎﻓ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻹﯾﺠﺎد‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ھﺬه‬ ‫ﺗﺴﺘﺨﺪم‬‫اﻟﺘﻮاﻟﻲ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺮﺑﻮطﺔ‬ ‫ﻣﺘﺴﻌﺎت‬ ‫ﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﺌﺔ‬

13. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-14-
‫ﺻﻔ‬ ‫ﺑﻴﻦ‬ ‫ﻋﺎزل‬ ‫إدﺧﺎل‬‫ﻣﺘﺴﻌﺔ‬ ‫ﻴﺤﺘﻲ‬‫واﺣﺪة‬‫ﻣﺘﻮاﻟﻴﺔ‬ ‫او‬ ‫ﻣﺘﻮازﻳﺔ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫ﻣﻦ‬ ‫اﻛﺜﺮ‬ ‫او‬:
‫ﻋﺰﻟﮭﺎ‬ ‫ﺛﺎﺑﺖ‬ ‫ﻋﺎزﻟﺔ‬ ‫ﻣﺎدة‬ ‫إدﺧﺎل‬ ‫ﻋﻨﺪ‬)k(‫ﻓﺎن‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬ ‫اﻛﺜﺮ‬ ‫او‬ ‫واﺣﺪة‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬:
1-‫اﻟﻌﺎزل‬ ‫إدﺧﺎل‬ ‫ﺑﻌﺪ‬ ‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬)Ceqk(‫ﺾ‬‫وﺑﻐ‬ ‫ﺎزل‬‫اﻟﻌ‬ ‫ﺎ‬‫ﻋﻠﯿﮭ‬ ‫ﻞ‬‫ادﺧ‬ ‫ﻲ‬‫اﻟﺘ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻌﺔ‬‫ﺳ‬ ‫ﺎدة‬‫زﯾ‬ ‫ﺴﺒﺐ‬‫ﺑ‬ ‫ﺰداد‬‫ﺗ‬ ‫ﺳﻮف‬
‫اﻟﻨﻈ‬‫ﺮ‬‫ا‬ ‫ﻛﻮن‬ ‫ﻋﻦ‬‫ﻮاﻟﻲ‬‫ﺗ‬ ‫او‬ ‫ﻮازي‬‫ﺗ‬ ‫ﺮﺑﻂ‬‫اﻟ‬ ‫ﻮن‬‫اوﻛ‬ ‫ﺼﻠﺔ‬‫ﻣﻨﻔ‬ ‫او‬ ‫ﺼﻠﺔ‬‫ﻣﺘ‬ ‫ﻟﻤﺠﻤﻮﻋﺔ‬‫ﺼﺒﺢ‬‫وﺗ‬)Ceqk > Ceq(‫ﻦ‬‫ﻣ‬ ‫ﺎ‬‫اﻣ‬ ‫ﺴﺐ‬‫وﺗﺤ‬
‫اﻟﻘﺎﻧﻮن‬)
Tk
Tk
eqk
V
Q
C
∆
=(‫اﻟﺮﺑﻂ‬ ‫ﺧﻮاص‬ ‫ﻣﻦ‬ ‫او‬)‫اﻟﺘﻮاﻟﻲ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬ ‫ﺑﺎﻟﻤﻘﻠﻮب‬ ‫او‬ ‫اﻟﺘﻮازي‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬ ‫ﺑﺎﻟﻤﺠﻤﻮع‬.(
2-‫ﺎزل‬‫اﻟﻌ‬ ‫ﻮد‬‫ﺑﻮﺟ‬ ‫ﺔ‬‫اﻟﻜﻠﯿ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬)QTk(‫ﺰداد‬‫ﺗ‬)QTk > QT(‫اﻟﺠ‬ ‫ﺮق‬‫ﻓ‬ ‫ﺖ‬‫وﯾﺜﺒ‬‫ﺪ‬‫ﺑﻌ‬ ‫ﻲ‬‫اﻟﻜﻠ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ان‬ ‫أي‬ ‫ﻲ‬‫اﻟﻜﻠ‬ ‫ﺪ‬‫ﮭ‬
‫ﺎزل‬ ‫اﻟﻌ‬ ‫ﻞ‬‫ﻗﺒ‬ ‫ﻲ‬ ‫اﻟﻜﻠ‬ ‫ﺪ‬ ‫اﻟﺠﮭ‬ ‫ﺮق‬ ‫ﻓ‬ ‫ﺴﺎوي‬ ‫ﯾ‬ ‫ﺎزل‬ ‫اﻟﻌ‬)TTk VV ∆=∆(‫ﺖ‬ ‫ﺗﺜﺒ‬ ‫او‬ ‫ﺔ‬ ‫ﺑﺎﻟﺒﻄﺎرﯾ‬ ‫ﺼﻠﺔ‬ ‫ﻣﺘ‬ ‫ﺔ‬ ‫اﻟﻤﺠﻤﻮﻋ‬ ‫ﻮن‬ ‫ﺗﻜ‬ ‫ﺪﻣﺎ‬ ‫ﻋﻨ‬
‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬‫اﻟﻌﺎزل‬ ‫ﻗﺒﻞ‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺗﺴﺎوي‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ان‬ ‫أي‬)TTk QQ =(‫ﺮق‬‫ﻓ‬ ‫ﻞ‬‫وﯾﻘ‬‫ﻲ‬‫اﻟﻜﻠ‬ ‫ﺪ‬‫اﻟﺠﮭ‬
)TTk VV ∆<∆(‫اﻟﺒﻄﺎرﯾﺔ‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬.
3-‫ﺔ‬‫اﻟﻜﻠﯿ‬ ‫ﺸﺤﻨﺔ‬‫واﻟ‬ ‫ﺗﻮازي‬ ‫اﻟﺮﺑﻂ‬ ‫ﻛﺎن‬ ‫اذا‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﻛﻞ‬ ‫ﺟﮭﺪ‬ ‫ﻓﺮق‬ ‫ﯾﺴﺎوي‬ ‫اﻟﻜﻠﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫اﻟﻌﺎزل‬ ‫إدﺧﺎل‬ ‫ﺑﻌﺪ‬
‫اﻟﻨ‬ ‫ﺾ‬‫وﺑﻐ‬ ‫ﻮاﻟﻲ‬‫ﺗ‬ ‫ﺮﺑﻂ‬‫اﻟ‬ ‫ﺎن‬‫ﻛ‬ ‫اذا‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﻛﻞ‬ ‫ﺷﺤﻨﺔ‬ ‫ﺗﺴﺎوي‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬‫ام‬ ‫ﺼﻠﺔ‬‫ﻣﺘ‬ ‫ﺔ‬‫اﻟﻤﺠﻤﻮﻋ‬ ‫ﻮن‬‫ﻛ‬ ‫ﻦ‬‫ﻋ‬ ‫ﺮ‬‫ﻈ‬
‫ﻣﻨﻔﺼﻠﺔ‬.
‫ان‬ ‫أي‬:
n21Tk V........VVV ∆=∆=∆=∆ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫ام‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﻛﻮن‬ ‫ﻋﻦ‬ ‫اﻟﻨﻈﺮ‬ ‫وﺑﻐﺾ‬ ‫ﻟﻠﺘﻮازي‬
or
n21Tk Q...........QQQ === ‫ﻣﻨﻔﺼﻠﺔ‬ ‫ام‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﻛﻮن‬ ‫ﻋﻦ‬ ‫اﻟﻨﻈﺮ‬ ‫وﺑﻐﺾ‬ ‫ﻟﻠﺘﻮاﻟﻲ‬
4-‫اﻟﻌ‬ ‫ﺑﻌﺪ‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺗﺜﺒﺖ‬ ‫اﻟﺤﺎﻻت‬ ‫ﻣﻦ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬‫ﺔ‬‫اﻟﻤﺠﻤﻮﻋ‬ ‫ﺖ‬‫ﻛﺎﻧ‬ ‫اذا‬ ‫ﺴﻌﺎت‬‫اﻟﻤﺘ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺴﻌﺔ‬‫ﻣﺘ‬ ‫ﻛﻞ‬ ‫ﺷﺤﻨﺔ‬ ‫ﺗﺴﺎوي‬ ‫ﺛﻢ‬ ‫ﺎزل‬
‫ﺴﺎوي‬‫ﺗ‬ ‫ﻢ‬‫ﺛ‬ ‫ﻦ‬‫وﻣ‬ ‫ﺎزل‬‫اﻟﻌ‬ ‫ﺎل‬‫إدﺧ‬ ‫ﺑﻌﺪ‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺗﺰداد‬ ‫اﺧﺮى‬ ‫ﺣﺎﻟﺔ‬ ‫وﻓﻲ‬ ‫اﻟﺘﻮاﻟﻲ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺮﺑﻂ‬ ‫وﻛﺎن‬ ‫اﻟﺒﻄﺎرﯾﺔ‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬
‫ﺗﻮاﻟﻲ‬ ‫اﻟﺮﺑﻂ‬ ‫وﻛﺎن‬ ‫ﺑﺎﻟﺒﻄﺎرﯾﺔ‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﻛﻞ‬ ‫ﺷﺤﻨﺔ‬.
5-‫ﻣﻦ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬‫ﺖ‬‫ﻛﺎﻧ‬ ‫اذا‬ ‫ﺴﻌﺎت‬‫اﻟﻤﺘ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺴﻌﺔ‬‫ﻣﺘ‬ ‫ﻞ‬‫ﻛ‬ ‫ﺪ‬‫ﺟﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﺴﺎوي‬‫ﯾ‬ ‫ﻢ‬‫ﺛ‬ ‫ﺎزل‬‫اﻟﻌ‬ ‫ﺪ‬‫ﺑﻌ‬ ‫ﻲ‬‫اﻟﻜﻠ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﯾﺜﺒﺖ‬ ‫اﻟﺤﺎﻻت‬
‫ﻣﺘﺴﻌﺔ‬ ‫ﻛﻞ‬ ‫ﺟﮭﺪ‬ ‫ﻓﺮق‬ ‫ﯾﺴﺎوي‬ ‫ﺛﻢ‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﻜﻠﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﯾﻘﻞ‬ ‫اﺧﺮى‬ ‫ﺣﺎﻟﺔ‬ ‫وﻓﻲ‬ ‫ﺗﻮازي‬ ‫اﻟﺮﺑﻂ‬ ‫وﻛﺎن‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺠﻤﻮﻋﺔ‬
‫ﺗﻮازي‬ ‫اﻟﺮﺑﻂ‬ ‫وﻛﺎن‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬.
6-‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬‫اﻟﻌﻼﻗﺎت‬ ‫ﻧﺘﺠﻨﺐ‬ ‫ان‬ ‫ﻋﻠﯿﻨﺎ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫رﺑﻂ‬)Qk=kQ‫و‬
k
V
Vk
∆
=∆‫و‬
k
E
Ek =(‫ﺎ‬‫ﻟﻜﻮﻧﮭ‬
‫ﺧﺎﺻﺔ‬ ‫ﺣﺎﻻت‬ ‫ﻓﻲ‬ ‫ﺗﻄﺒﻖ‬.
‫ﺣﻞ‬ ‫ﻋﻨﺪ‬ ‫ﻟﻬﺎ‬ ‫اﻻﻟﺘﻔﺎت‬ ‫ﻳﺠﺐ‬ ‫ﻣﻼﺣﻈﺎت‬‫ﺑﻌﺾ‬‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﺴﺎﺋﻞ‬:
1-‫اﻟﻌﺎ‬ ‫ﻗﺒﻞ‬ ‫اﻟﺴﻌﺔ‬ ‫اﻟﻰ‬ ‫ﺗﻀﺎف‬ ‫اﻟﻌﺎزل‬ ‫إدﺧﺎل‬ ‫ﺑﻌﺪ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻓﻲ‬ ‫اﻟﺰﯾﺎدة‬ ‫ﻣﻘﺪار‬ ‫ان‬‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻟﻠﺤﺼﻮل‬ ‫زل‬.
2-‫ﺎزل‬‫اﻟﻌ‬ ‫ﺪ‬‫ﺑﻌ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﺼﻮل‬‫ﻟﻠﺤ‬ ‫ﺎزل‬‫اﻟﻌ‬ ‫ﻞ‬‫ﻗﺒ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﻰ‬‫اﻟ‬ ‫ﻀﺎف‬‫ﺗ‬ ‫ﺎزل‬‫اﻟﻌ‬ ‫ﺎل‬‫إدﺧ‬ ‫ﺪ‬‫ﺑﻌ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﻓﻲ‬ ‫اﻟﺰﯾﺎدة‬ ‫ﻣﻘﺪار‬ ‫ان‬
)‫ﺑﺎﻟﻤﺼﺪر‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫او‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬ ‫ﺑﺎﻟﺸﺤﻨﺔ‬ ‫اﻟﺰﯾﺎدة‬ ‫ﺗﺤﺼﻞ‬ ‫ﺣﯿﺚ‬.(
3-‫اﻻﻧﺨﻔﺎض‬ ‫او‬ ‫اﻟﻨﻘﺼﺎن‬ ‫ﻣﻘﺪار‬ ‫ان‬‫ﻰ‬‫ﻋﻠ‬ ‫ﺼﻮل‬‫ﻟﻠﺤ‬ ‫ﺎزل‬‫اﻟﻌ‬ ‫ﻞ‬‫ﻗﺒ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻣﻦ‬ ‫ﯾﻄﺮح‬ ‫اﻟﻌﺎزل‬ ‫إدﺧﺎل‬ ‫ﺑﻌﺪ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻓﻲ‬
‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬)‫ﻦ‬‫ﻋ‬ ‫ﺼﻠﺔ‬‫ﻣﻨﻔ‬ ‫ﺴﻌﺎت‬‫اﻟﻤﺘ‬ ‫ﺔ‬‫ﻣﺠﻤﻮﻋ‬ ‫او‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻮن‬‫ﺗﻜ‬ ‫ﺪﻣﺎ‬‫ﻋﻨ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻓﻲ‬ ‫ﻧﻘﺼﺎن‬ ‫ﯾﺤﺼﻞ‬ ‫ﺣﯿﺚ‬
‫اﻟﻤﺼﺪر‬.(
‫اﻟﻤﺘﺴﻌﺔ‬ ‫وﺗﻔﺮﻳﻎ‬ ‫ﺷﺤﻦ‬:
‫اوﻻ‬:‫اﻟﺸﺤﻦ‬ ‫ﻣﺮﺣﻠﺔ‬:
a–‫اﻟﻤﻔﺘﺎح‬ ‫ﻏﻠﻖ‬ ‫ﻟﺤﻈﺔ‬
1-‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬‫اﻟﻤﻘﺎوﻣﺔ‬ ‫طﺮﻓﻲ‬ ‫ﻋﻠﻰ‬)RV∆(‫اﻟﺒﻄﺎرﯾﺔ‬ ‫ﺟﮭﺪ‬ ‫ﻓﺮق‬ ‫وﯾﺴﺎوي‬ ‫ﯾﻤﻜﻦ‬ ‫ﻣﺎ‬ ‫اﻋﻈﻢ‬)batteryV∆(.‫ان‬ ‫أي‬:
batteryR VV ∆=∆

14. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-15-
2-‫اﻟﺪاﺋﺮة‬ ‫ﺗﯿﺎر‬)‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺷﺤﻦ‬ ‫ﺗﯿﺎر‬(‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫اوم‬ ‫ﻟﻘﺎﻧﻮن‬ ‫وﻓﻘﺎ‬ ‫وﯾﺤﺴﺐ‬ ‫ﯾﻤﻜﻦ‬ ‫ﻣﺎ‬ ‫اﻋﻈﻢ‬:
3-‫ﺔ‬‫واﻟﻄﺎﻗ‬ ‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬‫واﻟﻤﺠ‬ ‫ﺼﻔﯿﺤﺘﯿﻦ‬‫اﻟ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫وﻓ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﻦ‬‫ﻣ‬ ‫أي‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬
‫ﺻﻔﺮ‬ ‫ﺗﺴﺎوي‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬.‫ان‬ ‫أي‬:
b-‫اﻟﺸﺤﻦ‬ ‫ﻋﻤﻠﯿﺔ‬ ‫اﻛﺘﻤﺎل‬ ‫ﺑﻌﺪ‬:
1-‫طﺮﻓﻲ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﯾﻨﻌﺪم‬‫ﺻﻔﺮ‬ ‫ﯾﺴﺎوي‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻓﻲ‬ ‫اﻟﺘﯿﺎر‬ ‫ﯾﺠﻌﻞ‬ ‫ﻣﻤﺎ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻓﻲ‬ ‫اﻟﻤﻘﺎوﻣﺔ‬.‫ان‬ ‫أي‬:
2-‫اﻟﺒﻄﺎرﯾﺔ‬ ‫ﺟﮭﺪ‬ ‫ﻓﺮق‬ ‫ﯾﺴﺎوي‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬)‫ﯾﻤﻜﻦ‬ ‫ﻣﺎ‬ ‫اﻋﻈﻢ‬. (‫ان‬ ‫أي‬:
3-‫ﻲ‬‫ﻓ‬ ‫ﺔ‬‫اﻟﻤﺨﺘﺰﻧ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬‫ﻦ‬‫ﻣ‬ ‫أي‬‫اﻟ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬‫واﻟﻤﺠ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬‫ﻲ‬‫ﻓ‬ ‫ﺔ‬‫اﻟﻤﺨﺘﺰﻧ‬ ‫ﺔ‬‫واﻟﻄﺎﻗ‬ ‫ﺼﻔﯿﺤﺘﯿﻦ‬
‫ﯾﻤﻜﻦ‬ ‫ﻣﺎ‬ ‫اﻋﻈﻢ‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬.‫ان‬ ‫أي‬:
‫ﻣﻼﺣﻈﺔ‬/‫رﺑﻄﻬـﺎ‬ ‫ﻋﻨـﺪ‬ ‫اﻣـﺎ‬ ‫اﻟﺒﻄﺎرﻳـﺔ‬ ‫ﺟﻬﺪ‬ ‫ﻓﺮق‬ ‫ﺗﺎﺧﺬ‬ ‫اﻟﺸﺤﻦ‬ ‫ﺑﻌﺪ‬ ‫ﻓﺎﻧﻬﺎ‬ ‫وﺑﻄﺎرﻳﺔ‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﻣﻊ‬ ‫اﻟﺘﻮاﻟﻲ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺘﺴﻌﺔ‬ ‫رﺑﻂ‬ ‫ﻋﻨﺪ‬
‫ﻣﻘﺎوﻣﺔ‬ ‫أي‬ ‫ﻣﻊ‬ ‫اﻟﺘﻮازي‬ ‫ﻋﻠﻰ‬‫اﻟﺪ‬ ‫ﻣﻘﺎوﻣﺎت‬ ‫ﻣﻦ‬‫اﺋﺮة‬‫اﻟﻤﻘﺎوﻣﺔ‬ ‫ﺗﻠﻚ‬ ‫ﺟﻬﺪ‬ ‫ﻓﺮق‬ ‫ﺗﺎﺧﺬ‬ ‫ﻓﺎﻧﻬﺎ‬.
‫ﺛﺎﻧﻴﺎ‬:‫اﻟ‬ ‫ﻣﺮﺣﻠﺔ‬‫ﺘﻔﺮﻳﻎ‬:
‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺗﻔﺮﯾﻎ‬ ‫ﺗﯿﺎر‬‫ﯾﺤﺴﺐ‬‫اﻟﺘﺎﻟﯿﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺔ‬ ‫ﻟﻠﻌﻼﻗﺔ‬ ‫وﻓﻘﺎ‬:
‫ﺣﯿﺚ‬:
I:، ‫اﻟﺘﻔﺮﯾﻎ‬ ‫ﺗﯿﺎر‬R:، ‫اﻟﺪاﺋﺮة‬ ‫ﻣﻘﺎوﻣﺔ‬∆VC:‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬
C
Q
2
1
PEor)V.(C
2
1
PEorQ.V
2
1
PE
d
V
E,V.CQ
2
2
CC
C
C
=∆=∆=
∆
=∆=
0I,0VR ==∆
0PE,0E,0V,0Q C ===∆=
R
V
I
battery∆
=
R
V
I C∆
=
batteryC VV ∆=∆

15. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-16-
‫ﺔ‬‫اﻟﻤﺘﻘﺎﺑﻠ‬ ‫ﺴﺎﺣﺔ‬‫اﻟﻤ‬ ‫ﺎدة‬‫زﯾ‬ ‫او‬ ‫ﻔﯿﺤﺘﯿﮭﺎ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺪ‬‫اﻟﺒﻌ‬ ‫ﺼﺎن‬‫ﻧﻘ‬ ‫او‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫ﻋﺎزل‬ ‫إدﺧﺎل‬ ‫ﺗﺄﺛﯿﺮ‬ ‫ﯾﺒﯿﻦ‬ ‫ﺟﺪول‬
‫ﺔ‬‫واﻟﻄﺎﻗ‬ ‫ﻔﯿﺤﺘﯿﮭﺎ‬‫ﺻ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫واﻟﻤﺠﺎل‬ ‫ﺻﻔﯿﺤﺘﯿﮭﺎ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺠﮭﺪ‬ ‫وﻓﺮق‬ ‫وﺷﺤﻨﺘﮭﺎ‬ ‫ﺳﻌﺘﮭﺎ‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬ ‫ﻋﻠﻰ‬ ‫ﻟﺼﻔﯿﺤﺘﯿﮭﺎ‬
‫اﻷو‬ ‫ﺎﻟﺘﯿﻦ‬ ‫ﺣ‬ ‫ﻲ‬ ‫ﻓ‬ ‫ﺼﻔﯿﺤﺘﯿﻦ‬ ‫اﻟ‬ ‫ﯿﻦ‬ ‫ﺑ‬ ‫ﺎﺋﻲ‬ ‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬ ‫اﻟﻤﺠ‬ ‫ﻲ‬ ‫ﻓ‬ ‫ﺔ‬ ‫اﻟﻤﺨﺘﺰﻧ‬‫ﻦ‬ ‫ﻋ‬ ‫ﺼﻠﺔ‬ ‫ﻣﻨﻔ‬ ‫ﺔ‬ ‫واﻟﺜﺎﻧﯿ‬ ‫ﺼﺪر‬ ‫ﺑﺎﻟﻤ‬ ‫ﺼﻠﺔ‬ ‫ﻣﺘ‬ ‫ﻰ‬ ‫ﻟ‬
‫اﻟﻤﺼﺪر‬.
‫ﲟﺼﺪﺭ‬ ‫ﻣﺘﺼﻠﺔ‬ ‫ﺍﳌﺘﺴﻌﺔ‬‫ﺍﳌﺼﺪﺭ‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫ﺍﳌﺘﺴﻌﺔ‬
‫ﺻﻔﻴﺤﺘﻴﻬﺎ‬ ‫ﺑﲔ‬ ‫ﻋﺎﺯﻟﺔ‬ ‫ﻣﺎﺩﺓ‬ ‫ﺇﺩﺧﺎﻝ‬
1‫اﻟﺴﻌﺔ‬:‫ﻻن‬ ‫ﺗﺰداد‬CK = K C‫اﻟﺴﻌﺔ‬:‫ﻻن‬ ‫ﺗﺰداد‬CK = K C
2
‫اﻟﺸﺤﻨﺔ‬:‫ﺗﺰداد‬ ‫اﻟﺴﻌﺔ‬ ‫ﻻن‬ ‫ﺗﺰداد‬)‫طﺮدي‬ ‫ﺗﻨﺎﺳﺐ‬(
‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬)∆V(
‫اﻟﺸﺤﻨﺔ‬:‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻻن‬ ‫ﺛﺎﺑﺘﺔ‬ ‫ﺗﺒﻘﻰ‬
3‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬:‫اﻟﻤﺼﺪر‬ ‫ﻟﻮﺟﻮد‬ ‫ﺛﺎﺑﺖ‬ ‫ﯾﺒﻘﻰ‬
‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬:‫ﺗﺰداد‬ ‫اﻟﺴﻌﺔ‬ ‫ﻻن‬ ‫ﯾﻘﻞ‬)‫ﻋﻜﺴﻲ‬ ‫ﺗﻨﺎﺳﺐ‬(
‫اﻟﺸﺤﻨﺔ‬ ‫ﺑﺜﺒﻮت‬)Q(
4
‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬:‫واﻟﺒﻌﺪ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻟﺜﺒﻮت‬ ‫ﺛﺎﺑﺖ‬
‫ﺣﯿﺚ‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬:
d
V
E
∆
=
‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬:‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻧﻘﺼﺎن‬ ‫ﺑﺴﺒﺐ‬ ‫ﯾﻘﻞ‬
)‫طﺮدي‬ ‫ﺗﻨﺎﺳﺐ‬(‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺒﻌﺪ‬ ‫ﺑﺜﺒﻮت‬)d(
5
‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬:‫اﻟﺸﺤﻨﺔ‬ ‫زﯾﺎدة‬ ‫ﺑﺴﺒﺐ‬ ‫ﺗﺰداد‬)‫ﺗﻨﺎﺳﺐ‬
‫طﺮدي‬(‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬)∆V(
‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬:‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻧﻘﺼﺎن‬ ‫ﺑﺴﺒﺐ‬ ‫ﺗﻘﻞ‬
)‫طﺮدي‬ ‫ﺗﻨﺎﺳﺐ‬(‫اﻟﺸﺤﻨﺔ‬ ‫ﺑﺜﺒﻮت‬)Q(
‫ﺻﻔﻴﺤﺘﻴﻬﺎ‬ ‫ﺑﲔ‬ ‫ﺍﻟﺒﻌﺪ‬ ‫ﻧﻘﺼﺎﻥ‬
1‫اﻟﺴﻌﺔ‬:‫ﻻن‬ ‫ﺗﺰداد‬
d
1
Cα‫اﻟﺴﻌﺔ‬:‫ﻻن‬ ‫ﺗﺰداد‬
d
1
Cα
2
‫اﻟﺸﺤﻨﺔ‬:‫ﺗﺰداد‬ ‫اﻟﺴﻌﺔ‬ ‫ﻻن‬ ‫ﺗﺰداد‬)‫طﺮدي‬ ‫ﺗﻨﺎﺳﺐ‬(
‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬)∆V(
‫اﻟﺸﺤﻨﺔ‬:‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻻن‬ ‫ﺛﺎﺑﺘﺔ‬ ‫ﺗﺒﻘﻰ‬
3‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬:‫اﻟﻤﺼﺪر‬ ‫ﻟﻮﺟﻮد‬ ‫ﺛﺎﺑﺖ‬ ‫ﯾﺒﻘﻰ‬
‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬:‫ﻻ‬ ‫ﯾﻘﻞ‬‫ﺗﺰداد‬ ‫اﻟﺴﻌﺔ‬ ‫ن‬)‫ﻋﻜﺴﻲ‬ ‫ﺗﻨﺎﺳﺐ‬(
‫اﻟﺸﺤﻨﺔ‬ ‫ﺑﺜﺒﻮت‬)Q(
4
‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬:‫ﺑﯿﻦ‬ ‫اﻟﺒﻌﺪ‬ ‫ﻟﻨﻘﺼﺎن‬ ‫ﯾﺰداد‬
‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬)‫ﻋﻜﺴﻲ‬ ‫ﺗﻨﺎﺳﺐ‬(‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬
)∆V(
‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬:‫ﯾﻘﻞ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻻن‬ ‫ﺛﺎﺑﺖ‬ ‫ﯾﺒﻘﻰ‬
‫وان‬ ‫ﯾﻘﻞ‬ ‫واﻟﺒﻌﺪ‬
d
V
E
∆
=
5
‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬:‫زﯾﺎد‬ ‫ﺑﺴﺒﺐ‬ ‫ﺗﺰداد‬‫اﻟﺸﺤﻨﺔ‬ ‫ة‬
)‫طﺮدي‬ ‫ﺗﻨﺎﺳﺐ‬(‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬)∆V(
‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬:‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻧﻘﺼﺎن‬ ‫ﺑﺴﺒﺐ‬ ‫ﺗﻘﻞ‬
)‫طﺮدي‬ ‫ﺗﻨﺎﺳﺐ‬(‫اﻟﺸﺤﻨﺔ‬ ‫ﺑﺜﺒﻮت‬)Q(
‫ﻟﻠﺼﻔﻴﺤﺘﲔ‬ ‫ﺍﳌﺘﻘﺎﺑﻠﺔ‬ ‫ﺍﳌﺴﺎﺣﺔ‬ ‫ﺯﻳﺎﺩﺓ‬
1‫اﻟﺴﻌﺔ‬:‫ﻻن‬ ‫ﺗﺰداد‬ACα‫اﻟﺴﻌﺔ‬:‫ﻻن‬ ‫ﺗﺰداد‬ACα
2
‫اﻟﺸﺤﻨﺔ‬:‫ﺗﺰدا‬‫ﺗﺰداد‬ ‫اﻟﺴﻌﺔ‬ ‫ﻻن‬ ‫د‬)‫طﺮدي‬ ‫ﺗﻨﺎﺳﺐ‬(
‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬)∆V(
‫اﻟﺸﺤﻨﺔ‬:‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻻن‬ ‫ﺛﺎﺑﺘﺔ‬ ‫ﺗﺒﻘﻰ‬
3‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬:‫اﻟﻤﺼﺪر‬ ‫ﻟﻮﺟﻮد‬ ‫ﺛﺎﺑﺖ‬ ‫ﯾﺒﻘﻰ‬
‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬:‫ﺗﺰداد‬ ‫اﻟﺴﻌﺔ‬ ‫ﻻن‬ ‫ﯾﻘﻞ‬)‫ﻋﻜﺴﻲ‬ ‫ﺗﻨﺎﺳﺐ‬(
‫اﻟﺸﺤﻨﺔ‬ ‫ﺑﺜﺒﻮت‬)Q(
4
‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬:‫واﻟﺒﻌﺪ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻟﺜﺒﻮت‬ ‫ﺛﺎﺑﺖ‬
‫ﺑﯿﻦ‬‫ﺣﯿﺚ‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬:
d
V
E
∆
=
‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬:‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻧﻘﺼﺎن‬ ‫ﺑﺴﺒﺐ‬ ‫ﯾﻘﻞ‬
)‫طﺮدي‬ ‫ﺗﻨﺎﺳﺐ‬(‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺒﻌﺪ‬ ‫ﺑﺜﺒﻮت‬)d(
5
‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬:‫اﻟﺸﺤﻨﺔ‬ ‫زﯾﺎدة‬ ‫ﺑﺴﺒﺐ‬ ‫ﺗﺰداد‬
)‫طﺮدي‬ ‫ﺗﻨﺎﺳﺐ‬(‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬)∆V(
‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬:‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻧﻘﺼﺎن‬ ‫ﺑﺴﺒﺐ‬ ‫ﺗﻘﻞ‬
)‫ﺗ‬‫طﺮدي‬ ‫ﻨﺎﺳﺐ‬(‫اﻟﺸﺤﻨﺔ‬ ‫ﺑﺜﺒﻮت‬)Q(

16. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-17-
‫ﺍﻟﻌﺎﺯﻝ‬ ‫ﺍﺩﺧﺎﻝ‬ ‫ﺑﻌﺪ‬ ‫ﺍﳊﻞ‬ ‫ﺧﻄﻮﺍﺕ‬
‫ﺍﻟﻔﺼﻞ‬ ‫ﲤﺎﺭﻳﻦ‬ ‫ﻣﻦ‬ ‫ﺍﻟﺜﺎﻧﻲ‬ ‫ﻭﺍﻟﺴﺆﺍﻝ‬ ‫ﺍﻷﻭﻝ‬ ‫ﺍﳌﺜﺎﻝ‬ ‫ﰲ‬ ‫ﻛﻤﺎ‬ ‫ﺍﻟﻮﺍﺣﺪﺓ‬ ‫ﻟﻠﻤﺘﺴﻌﺔ‬:
‫اﻟﻌﺰل‬ ‫ﺛﺎﺑﺖ‬ ‫ﻛﻮن‬ ‫ﻋﻠﻰ‬ ‫ﯾﻌﺘﻤﺪ‬ ‫واﻟﺤﻞ‬ ‫اﻟﻌﺎزل‬ ‫إدﺧﺎل‬ ‫ﺑﻌﺪ‬ ‫ﺑﺨﻄﻮﺗﯿﻦ‬ ‫ﯾﺤﻞ‬ ‫اﻟﻤﺴﺎﺋﻞ‬ ‫ﻣﻦ‬ ‫اﻟﻨﻮع‬ ‫ھﺬا‬)k(‫ﻣﺠﮭﻮل‬ ‫ام‬ ‫ﻣﻌﻠﻮم‬
‫اوﻻ‬:‫اﻟﻌﺰل‬ ‫ﺛﺎﺑﺖ‬ ‫ﯾﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬)k(‫ھﻲ‬ ‫اﻟﺤﻞ‬ ‫ﺧﻄﻮات‬ ‫ﻓﺎن‬ ‫ﻣﻌﻠﻮم‬:
1- CK =KC
2-
K
K
K
V
Q
C
∆
=
♦‫اﻟﻌﺎزﻟﺔ‬ ‫اﻟﻤﺎدة‬ ‫ﺑﻮﺟﻮد‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬ ‫اﺳﺘﺨﺮاج‬ ‫اﻷوﻟﻰ‬ ‫ﻟﻠﺨﻄﻮة‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬.
♦‫ﻮد‬‫ﺑﻮﺟ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫او‬ ‫ﺎزل‬‫اﻟﻌ‬ ‫ﺑﻮﺟﻮد‬ ‫اﻟﺸﺤﻨﺔ‬ ‫اﻣﺎ‬ ‫اﺳﺘﺨﺮاج‬ ‫اﻟﺜﺎﻧﯿﺔ‬ ‫ﻟﻠﺨﻄﻮة‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻮن‬‫ﻛ‬ ‫ﺎة‬‫ﻣﺮاﻋ‬ ‫ﻊ‬‫ﻣ‬ ‫ﺎزل‬‫اﻟﻌ‬
‫ام‬ ‫ﺑﺎﻟﻤﺼﺪر‬ ‫ﻣﺘﺼﻠﺔ‬‫ﻋﻨﮫ‬ ‫ﻣﻨﻔﺼﻠﺔ‬.
‫ﺎزل‬‫اﻟﻌ‬ ‫ﻞ‬‫ﻗﺒ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻧﻔﺴﮫ‬ ‫ھﻮ‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻓﺎن‬ ‫ﺑﺎﻟﺒﻄﺎرﯾﺔ‬ ‫ﻣﺘﺼﻠﺔ‬ ‫زاﻟﺖ‬ ‫ﻣﺎ‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻓﻌﻨﺪﻣﺎ‬
)‫ﺛﺎﺑﺖ‬(‫اﻟﻌﺎزل‬ ‫ﻗﺒﻞ‬ ‫اﻟﺠﮭﺪ‬ ‫وﻓﺮق‬ ‫اﻻوﻟﻰ‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﻦ‬ ‫اﻟﺴﻌﺔ‬ ‫ﺑﻤﻌﺮﻓﺔ‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺗﺴﺘﺨﺮج‬ ‫ان‬ ‫اﻻ‬ ‫ﻋﻠﯿﻚ‬ ‫ﻓﻤﺎ‬.
‫وادﺧﻞ‬ ‫اﻟﺒﻄﺎرﯾﺔ‬ ‫ﻋﻦ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻓﺼﻞ‬ ‫وﻋﻨﺪ‬‫ﺤﻨﺘﮭﺎ‬‫ﺷ‬ ‫ﺖ‬‫ﺗﺜﺒ‬ ‫ﻔﯿﺤﺘﮭﺎ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫اﻟﻌﺎزل‬)‫ﻞ‬‫ﻗﺒ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﺴﺎوي‬‫ﺗ‬ ‫ﺎزل‬‫اﻟﻌ‬ ‫ﺪ‬‫ﺑﻌ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬
‫اﻟﻌﺎزل‬(‫ﻞ‬‫ﻗﺒ‬ ‫ﺸﺤﻨﺔ‬‫واﻟ‬ ‫ﻰ‬‫اﻻوﻟ‬ ‫ﺔ‬‫اﻟﻨﻘﻄ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﺳﻌﺔ‬ ‫ﺑﻤﻌﺮﻓﺔ‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺟﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺗﺴﺘﺨﺮج‬ ‫ان‬ ‫اﻻ‬ ‫ﻋﻠﯿﻚ‬ ‫وﻣﺎ‬
‫اﻟﻌﺎزل‬.
‫ﺛﺎﻧﯿﺎ‬:‫اﻟﻌﺰل‬ ‫ﺛﺎﺑﺖ‬ ‫ﯾﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬K‫اﻟﻤﺠﮭﻮل‬ ‫ھﻮ‬:
‫اﻟﺨﻄﻮ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺜﺎﻧﯿﺔ‬ ‫اﻟﺨﻄﻮة‬ ‫ﻧﻘﺪم‬‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﺎزل‬‫اﻟﻌ‬ ‫ﻮد‬‫ﺑﻮﺟ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﻗﺴﻤﺔ‬ ‫ﻣﻦ‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻮﺟﻮد‬ ‫اﻟﺴﻌﺔ‬ ‫ﻹﯾﺠﺎد‬ ‫اﻷوﻟﻰ‬ ‫ط‬
‫ﺔ‬ ‫ﺑﺎﻟﺒﻄﺎرﯾ‬ ‫ﺼﻠﺔ‬ ‫ﻣﺘ‬ ‫ﻞ‬‫ھ‬ ‫ﺴﻌﺔ‬ ‫اﻟﻤﺘ‬ ‫ﺔ‬ ‫ﻣﻌﺮﻓ‬ ‫ﺪ‬ ‫ﺑﻌ‬ ‫ﺎزل‬ ‫اﻟﻌ‬ ‫ﻮد‬ ‫ﺑﻮﺟ‬)‫ﺔ‬ ‫اﻟﺤﺎﻟ‬ ‫ﺬه‬ ‫ھ‬ ‫ﻲ‬ ‫ﻓ‬ ‫ﺪھﺎ‬ ‫ﺟﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﺖ‬‫ﯾﺜﺒ‬ ‫ﺚ‬‫ﺣﯿ‬(‫ﻦ‬ ‫ﻋ‬ ‫ﺼﻠﺔ‬ ‫ﻣﻨﻔ‬ ‫ام‬
‫اﻟﺒﻄﺎرﯾﺔ‬)‫اﻟﺤﺎﻟﺔ‬ ‫ھﺬه‬ ‫ﻓﻲ‬ ‫ﺷﺤﻨﺘﮭﺎ‬ ‫ﺗﺜﺒﺖ‬ ‫ﺣﯿﺚ‬.(
‫ﺗﻮﺍﱄ‬ ‫ﺃﻭ‬ ‫ﺗﻮﺍﺯﻱ‬ ‫ﻣﺮﺑﻮﻃﺔ‬ ‫ﺍﳌﺘﺴﻌﺎﺕ‬ ‫ﻣﻦ‬ ‫ﻤﻮﻉ‬‫ﻭﺍﳋﺎﻣﺲ‬ ‫ﻭﺍﻟﺮﺍﺑﻊ‬ ‫ﺍﻟﺜﺎﻟﺚ‬ ‫ﺍﻟﺴﺆﺍﻝ‬ ‫ﰲ‬ ‫ﻛﻤﺎ‬
‫ﻓﺮﻋﯿﺔ‬ ‫ﺧﻄﻮات‬ ‫ھﻲ‬ ‫واﻟﺒﻘﯿﺔ‬ ‫أﺳﺎﺳﯿﺔ‬ ‫ﺧﻄﻮات‬ ‫ﺛﻼث‬ ‫ﻋﻠﻰ‬ ‫ﻣﻌﺘﻤﺪا‬ ‫اﻟﺤﻞ‬ ‫ﯾﻜﻮن‬:
‫ﻋﻠﻰ‬ ‫ﻣﻌﺘﻤﺪة‬ ‫اﻷﺳﺎﺳﯿﺔ‬ ‫ﻓﺎﻟﺨﻄﻮات‬K‫ﻣﺠﮭﻮل‬ ‫ام‬ ‫ﻣﻌﻠﻮم‬
‫اوﻻ‬:‫ﯾﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬K‫اﻵﺗﯿﺔ‬ ‫اﻟﺨﻄﻮات‬ ‫ﻧﺘﺒﻊ‬ ‫ﻣﺜﻼ‬ ‫اﻷوﻟﻰ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻌﺎزل‬ ‫وادﺧﻞ‬ ‫ﻣﻌﻠﻮم‬:
1-‫ﻧﺠﺪ‬C1K‫اﻟﻌ‬ ‫ﻣﻦ‬‫ﻼﻗﺔ‬:C1K=KC1
2-‫ﺪ‬‫ﻧﺠ‬C(eq)k‫ﺴﻌﺎت‬‫اﻟ‬ ‫ﻮع‬ ‫ﻣﺠﻤ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﺎ‬ ‫اﻣ‬ ‫ﺮﺑﻂ‬‫اﻟ‬ ‫ﻮاص‬ ‫ﺧ‬ ‫ﻦ‬ ‫ﻣ‬)‫ﻮازي‬ ‫ﺗ‬ ‫ﺮﺑﻂ‬‫اﻟ‬ ‫ﺎن‬ ‫ﻛ‬ ‫اذا‬(‫ﺴﻌﺎت‬ ‫اﻟ‬ ‫ﻮع‬ ‫ﻣﺠﻤ‬ ‫ﻮب‬ ‫ﻣﻘﻠ‬ ‫ﻦ‬‫ﻣ‬ ‫او‬
)‫ﺗﻮاﻟﻲ‬ ‫اﻟﺮﺑﻂ‬ ‫ﻛﺎن‬ ‫اذا‬(
3-‫ﺎﻧﻮن‬ ‫اﻟﻘ‬ ‫ﺴﺘﺨﺪم‬ ‫ﻧ‬)
k)t(
k)t(
eqk
V
Q
C
∆
=(‫ﺎد‬ ‫ﻹﯾﺠ‬ ‫ﺎ‬ ‫أﻣ‬)QTK(‫ﺎد‬ ‫ﻹﯾﺠ‬ ‫أو‬)∆VTk(‫ﺼﻠﺔ‬ ‫ﻣﺘ‬ ‫ﺔ‬ ‫اﻟﻤﺠﻤﻮﻋ‬ ‫ﻞ‬ ‫ھ‬ ‫ﺔ‬ ‫ﻣﻌﺮﻓ‬ ‫ﺪ‬ ‫ﺑﻌ‬
‫ﺑﺎﻟﺒﻄﺎرﯾﺔ‬)‫ﺖ‬‫ﺛﺎﺑ‬ ‫اﻟﻜﻠﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﯾﺒﻘﻰ‬ ‫ﺣﯿﺚ‬(‫ﺎ‬‫ﻋﻨﮭ‬ ‫ﺼﻠﺔ‬‫ﻣﻨﻔ‬ ‫ام‬)‫ﺔ‬‫ﺛﺎﺑﺘ‬ ‫ﺔ‬‫اﻟﻜﻠﯿ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﻰ‬‫ﺗﺒﻘ‬ ‫ﺚ‬‫ﺣﯿ‬.(‫ﻰ‬‫ﻋﻠ‬ ‫ﺪ‬‫ﻧﻌﺘﻤ‬ ‫ﻚ‬‫ذﻟ‬ ‫ﺪ‬‫ﺑﻌ‬
‫ﻂ‬‫رﺑ‬ ‫ﻲ‬‫وﻓ‬ ‫ﺴﻌﺔ‬‫ﻣﺘ‬ ‫ﻞ‬‫ﻛ‬ ‫ﺪ‬‫ﺟﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﺴﺎوي‬‫ﯾ‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﻜﻠﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫اﻟﺘﻮازي‬ ‫رﺑﻂ‬ ‫ﻓﻔﻲ‬ ‫ﺗﻮاﻟﻲ‬ ‫أم‬ ‫ﺗﻮازي‬ ‫اﻟﺮﺑﻂ‬ ‫ﺧﻮاص‬
‫ﻣﺘﺴﻌﺔ‬ ‫ﻛﻞ‬ ‫ﺷﺤﻨﺔ‬ ‫ﺗﺴﺎوي‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫ﻛﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫اﻟﺘﻮاﻟﻲ‬.
‫ﺛﺎﻧﯿﺎ‬:‫ﯾﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬K‫ﻧﺘﺒﻊ‬ ‫ﻣﺜﻼ‬ ‫اﻷوﻟﻰ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻌﺰل‬ ‫وادﺧﻞ‬ ‫ﻣﺠﮭﻮل‬‫ﻧﻔﺲ‬‫اﻟﺨﻄﻮة‬ ‫ﻧﺠﻌﻞ‬ ‫وﻟﻜﻦ‬ ‫اﻟﺨﻄﻮات‬‫ﻰ‬‫اﻻوﻟ‬
‫اﻻوﻟﻰ‬ ‫ھﻲ‬ ‫اﻟﺜﺎﻟﺜﺔ‬ ‫واﻟﺨﻄﻮة‬ ‫اﻟﺜﺎﻟﺜﺔ‬ ‫ھﻲ‬‫ﯾﺎﺗﻲ‬ ‫وﻛﻤﺎ‬:
1-‫ﺎﻧﻮن‬ ‫اﻟﻘ‬ ‫ﺴﺘﺨﺪم‬ ‫ﻧ‬)
k)t(
k)t(
eqk
V
Q
C
∆
=(‫ﺎد‬ ‫ﻻﯾﺠ‬C(eq)k‫ﺔ‬ ‫ﺑﺎﻟﺒﻄﺎرﯾ‬ ‫ﺼﻠﺔ‬ ‫ﻣﺘ‬ ‫ﺔ‬ ‫اﻟﻤﺠﻤﻮﻋ‬ ‫ﻞ‬ ‫ھ‬ ‫ﺔ‬ ‫ﻣﻌﺮﻓ‬ ‫ﺪ‬ ‫ﺑﻌ‬
)‫ﺛﺎﺑﺖ‬ ‫اﻟﻜﻠﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﯾﺒﻘﻰ‬ ‫ﺣﯿﺚ‬(‫ﻋﻨﮭﺎ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫ام‬)‫ﺛﺎﺑﺘﺔ‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺗﺒﻘﻰ‬ ‫ﺣﯿﺚ‬. (
2-‫ﺗﻮازي‬ ‫اﻟﺮﺑﻂ‬ ‫ﺧﻮاص‬ ‫ﻧﺴﺘﺨﺪم‬)‫ﺴﻌﺎت‬‫اﻟ‬ ‫ﻣﺠﻤﻮع‬(‫ﻮاﻟﻲ‬‫اﻟﺘ‬ ‫او‬)‫ﺴﻌﺎت‬‫اﻟ‬ ‫ﻮب‬‫ﻣﻘﻠ‬(‫ﻞ‬‫ادﺧ‬ ‫ﻲ‬‫واﻟﺘ‬ ‫ﺔ‬‫اﻟﻤﺠﮭﻮﻟ‬ ‫ﺴﻌﺔ‬‫اﻟ‬ ‫ﺎد‬‫ﻻﯾﺠ‬
‫اﻟﻌﺎزل‬ ‫ﻋﻠﯿﮭﺎ‬.
3-‫ﻧﺠﺪ‬K‫اﻟﻌﻼﻗﺔ‬ ‫ﻣﻦ‬:CK =KC.

17. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-18-
‫اﻻول‬ ‫اﻟﻔﺼﻞ‬ ‫ﻗﻮاﻧﻴﻦ‬
‫اوﻻ‬:‫واﺣﺪة‬ ‫ﻣﺘﺴﻌﺔ‬
♦‫ﻫﻮاء‬ ‫او‬ ‫ﻓﺮاغ‬ ‫اﻟﻌﺎزل‬ ‫ﻛﺎن‬ ‫اذا‬)‫اﻟﻌﺎزل‬ ‫ادﺧﺎل‬ ‫ﻗﺒﻞ‬(:
,
♦‫اﻟﻬﻮاء‬ ‫او‬ ‫اﻟﻔﺮاغ‬ ‫ﻏﻴﺮ‬ ‫اﻟﻌﺎزل‬ ‫ﻛﺎن‬ ‫اذا‬)‫اﻟﻌﺎزل‬ ‫ادﺧﺎل‬ ‫ﺑﻌﺪ‬(:
1(‫اﻟﻘﻮاﻧﻴﻦ‬:
,
2(‫اﻟﻌﻼﻗﺎت‬:
‫ﺑﺎﻟﻤﺼﺪر‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬
CkCk =CkCk =
QkQk =QQk =
VVk ∆=∆
k
V
Vk
∆
=∆
EEk =
k
E
Ek =
PEkPEk =
k
PE
PEk =
‫ﻣﺘﻮاﻟﻴﺔ‬ ‫او‬ ‫ﻣﺘﻮازﻳﺔ‬ ‫ﻣﺘﺴﻌﺎت‬ ‫ﻣﺠﻤﻮﻋﺔ‬‫وﻣﺘﻮاﻟﻴﺔ‬ ‫ﻣﺘﻮازﻳﺔ‬ ‫او‬)‫ﻣﺨﺘﻠﻂ‬(:
‫اوﻻ‬:‫اﻟﻘﻮاﻧﻴﻦ‬:
‫ﻛﺎن‬ ‫اذا‬‫ﻫﻮاء‬ ‫او‬ ‫ﻓﺮاغ‬ ‫اﻟﻌﺎزل‬)‫اﻟﻌﺎزل‬ ‫ادﺧﺎل‬ ‫ﻗﺒﻞ‬(:
eq
2
T
T
2
TeqTTTT
C
Q
.
2
1
PEor)V.(C
2
1
PEorQ.V
2
1
PE =∆=∆=
T
T
eq
V
Q
C
∆
=
k
2
k
k
2
kkkkkk
C
Q
.
2
1
PEor)V.(C
2
1
PEorQ.V
2
1
PE =∆=∆=
d
V
E k
k
∆
=d
A
kCor
V
Q
C k
k
k
k οε=
∆
=
C
Q
.
2
1
PEor)V.(C
2
1
PEorQ.V
2
1
PE
2
2
=∆=∆=
d
V
E
∆
=
d
A
Cor
V
Q
C οε=
∆
=

18. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-19-
‫اﻟﻬﻮاء‬ ‫او‬ ‫اﻟﻔﺮاغ‬ ‫ﻏﻴﺮ‬ ‫اﻟﻌﺎزل‬ ‫ﻛﺎن‬ ‫اذا‬)‫اﻟﻌﺎزل‬ ‫ادﺧﺎل‬ ‫ﺑﻌﺪ‬(:
‫ﺛﺎﻧﻴﺎ‬:‫اﻟﺨﻮاص‬
‫ت‬‫اﻟﺘﻮازي‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫رﺑﻂ‬‫اﻟﺘﻮاﻟﻲ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫رﺑﻂ‬
1
‫ﻌﺎت‬ ‫ﺳ‬ ‫ﻮع‬ ‫ﻣﺠﻤ‬ ‫ﺴﺎوي‬ ‫ﺗ‬ ‫ﺔ‬ ‫ﻟﻠﻤﺠﻤﻮﻋ‬ ‫ﺔ‬ ‫اﻟﻤﻜﺎﻓﺌ‬ ‫ﺴﻌﺔ‬ ‫اﻟ‬
‫ان‬ ‫أي‬ ‫اﻟﻤﺘﺴﻌﺎت‬:
Ceq=C1 + C2 + C3 + ……. Cn
‫ﻮع‬ ‫ﻣﺠﻤ‬ ‫ﺴﺎوي‬ ‫ﯾ‬ ‫ﺔ‬ ‫ﻟﻠﻤﺠﻤﻮﻋ‬ ‫ﺔ‬ ‫اﻟﻤﻜﺎﻓﺌ‬ ‫ﺴﻌﺔ‬ ‫اﻟ‬ ‫ﻮب‬ ‫ﻣﻘﻠ‬
‫ان‬ ‫أي‬ ‫اﻟﺴﻌﺎت‬ ‫ﻣﻘﻠﻮب‬:
n321eq
C
1
.......
C
1
C
1
C
1
C
1
+++=
2
‫اﻟ‬‫ان‬ ‫أي‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﺷﺤﻨﺎت‬ ‫ﻣﺠﻤﻮع‬ ‫ﺗﺴﺎوي‬ ‫اﻟﻜﻠﯿﺔ‬ ‫ﺸﺤﻨﺔ‬:
QT =Q1 + Q2 + Q3 + …….Qn
‫ﺴﻌﺎت‬‫اﻟﻤﺘ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺴﻌﺔ‬‫ﻣﺘ‬ ‫أي‬ ‫ﺤﻨﺔ‬‫ﺷ‬ ‫ﺴﺎوي‬‫ﺗ‬ ‫ﺔ‬‫اﻟﻜﻠﯿ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬
)‫ﺛﺎﺑﺘﺔ‬ ‫اﻟﺸﺤﻨﺔ‬(‫ان‬ ‫أي‬:
QT =Q1 = Q2 = Q3 = …….Qn
3
‫ﻦ‬ ‫ﻣ‬ ‫ﺴﻌﺔ‬ ‫ﻣﺘ‬ ‫أي‬ ‫ﺪ‬ ‫ﺟﮭ‬ ‫ﺮق‬ ‫ﻓ‬ ‫ﺴﺎوي‬ ‫ﯾ‬ ‫ﻲ‬ ‫اﻟﻜﻠ‬ ‫ﺪ‬ ‫اﻟﺠﮭ‬ ‫ﺮق‬ ‫ﻓ‬
‫اﻟﻤﺘﺴﻌﺎت‬)‫ﺛﺎﺑﺖ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬(‫ان‬ ‫أي‬:
∆VT =∆V1 = ∆V2 =∆V3 =…….∆Vn
‫ﻟﻠﻤﺘﺴﻌﺎت‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻣﺠﻤﻮع‬ ‫ﯾﺴﺎوي‬ ‫اﻟﻜﻠﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬
‫ان‬ ‫أي‬:
∆VT =∆V1 + ∆V2 + ∆V3 + ……. ∆Vn
4.........PEPEPEPE 321T +++=..........PEPEPEPE 321T +++=
5
‫اﻟﺴﻌﺔ‬ ‫اﻟﻤﺘﻤﺎﺛﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬ ‫ﻋﺪد‬ ‫ﻻي‬)‫اﻟﻤﺘﺴﺎوﯾﺔ‬(‫ﻓﺎن‬:
‫ﺔ‬ ‫اﻟﻤﻜﺎﻓﺌ‬ ‫ﺴﻌﺔ‬ ‫اﻟﻤﺘ‬ ‫ﻌﺔ‬ ‫ﺳ‬=‫ﺪد‬ ‫ﻋ‬‫ﺴﻌﺎت‬ ‫اﻟﻤﺘ‬×‫أي‬ ‫ﻌﺔ‬ ‫ﺳ‬
‫ﻣﺘﺴﻌﺘﺔ‬
nCCeq =
‫ﺴﻌﺔ‬ ‫اﻟ‬ ‫ﺔ‬ ‫اﻟﻤﺘﻤﺎﺛﻠ‬ ‫ﺴﻌﺎت‬ ‫اﻟﻤﺘ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﺪد‬ ‫ﻋ‬ ‫ﻻي‬)‫ﺴﺎوﯾﺔ‬ ‫اﻟﻤﺘ‬(
‫ﻓﺎن‬:
‫ﺔ‬ ‫اﻟﻤﻜﺎﻓﺌ‬ ‫ﺴﻌﺔ‬ ‫اﻟﻤﺘ‬ ‫ﻌﺔ‬ ‫ﺳ‬=‫ﺴﻌﺔ‬ ‫ﻣﺘ‬ ‫أي‬ ‫ﻌﺔ‬ ‫ﺳ‬/‫ﺪد‬ ‫ﻋ‬
‫اﻟﻤﺘﺴﻌﺎت‬
n
C
Ceq =
eqk
2
Tk
Tk
2
TkeqkTkTkTkTk
C
Q
.
2
1
PEor)V.(C
2
1
PEorQ.V
2
1
PE =∆=∆=
Tk
Tk
eqk
V
Q
C
∆
=
QTK = QT ‫ﻟﻠﻤﻨﻔﺼﻠﺔ‬ or ∆VTk = ∆VT ‫ﻟﻠﻤﺘﺼﻠﺔ‬ , Ck=k C
C1
C2
C3
∆VT
∆VT
C1 C2 C3

19. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-20-
‫اﻟﻤﺘﺴﻌﺔ‬ ‫وﺗﻔﺮﻳﻎ‬ ‫ﺷﺤﻦ‬:
‫اوﻻ‬:‫اﻟﻤﻔﺘﺎح‬ ‫ﻏﻠﻖ‬ ‫ﻟﺤﻈﺔ‬
0PE,0E,0V,0Q
R
V
I,VV
C
battery
batteryR
===∆=
∆
=∆=∆
‫ﺛﺎﻧﻴﺎ‬:‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺷﺤﻦ‬ ‫اﺗﻤﺎم‬ ‫ﺑﻌﺪ‬:
C
Q
2
1
PEor)V.(C
2
1
PEorQ.V
2
1
PE
,
d
V
E,V.CQ,VV
0I,0V
2
2
C
C
CbatteryC
R
=∆=∆=
∆
=∆=∆=∆
==∆
‫ﺛﺎﻧﻴﺎ‬:‫اﻵﺗﻴﺔ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﻣﻦ‬ ‫ﻳﺤﺴﺐ‬ ‫اﻟﺘﻔﺮﻳﻎ‬ ‫ﺗﻴﺎر‬:
R
V
I C∆
=

20. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻧﻲ‬:‫اﻟ‬‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻲ‬ ‫ﺤﺚ‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-21-
×
‫اﻟﻤﻐﻨﺎﻃﻴﺴﻴﺔ‬ ‫واﻟﻘﻮة‬ ‫اﻟﻜﻬﺮﺑﺎﺋﻴﺔ‬ ‫اﻟﻘﻮة‬:
‫ﻣﺸﺤﻮن‬ ‫ﺟﺴﻴﻢ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺆﺛﺮة‬ ‫اﻟﻜﻬﺮﺑﺎﺋﻴﺔ‬ ‫اﻟﻘﻮة‬ ‫ﻋﻦ‬ ‫ﻳﻌﺒﺮ‬‫وﻋﻦ‬ ‫ﻛﻬﺮﺑﺎﺋﻲ‬ ‫ﻣﺠﺎل‬ ‫داﺧﻞ‬ ‫ﻳﺘﺤﺮك‬‫اﻟﻤـﺆﺛﺮة‬ ‫اﻟﻤﻐﻨﺎﻃﻴـﺴﻴﺔ‬ ‫واﻟﻘﻮة‬
‫ﻣﺸﺤﻮن‬ ‫ﺟﺴﻴﻢ‬ ‫ﻋﻠﻰ‬‫ﻣﻐﻨﺎﻃﻴﺴﻲ‬ ‫ﻣﺠﺎل‬ ‫داﺧﻞ‬ ‫ﻳﺘﺤﺮك‬‫اﻻﺗﻴﺔ‬ ‫اﻟﺮﻳﺎﺿﻴﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺎت‬:
‫اﻟﻜﮭﺮﺑ‬ ‫اﻟﻘﻮة‬ ‫وﺣﺪة‬‫ﺎﺋﯿﺔ‬)FE(‫اﻟﻨﯿﻮﺗﻦ‬ ‫ھﻲ‬)N(‫ﺑﺎﻟﻜﻮﻟﻮم‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬)C(‫ﺑﻮﺣﺪة‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫واﻟﻤﺠﺎل‬)N/C.(
‫اﻵﺗﯿﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺔ‬ ‫ﻓﯿﻌﻄﻰ‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﯿﺔ‬ ‫اﻟﻘﻮة‬ ‫ﻣﻘﺪار‬ ‫اﻣﺎ‬:
‫ﺣﯿﺚ‬:
FB:‫ﺑﻮﺣﺪة‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﯿﺔ‬ ‫اﻟﻘﻮة‬)N(‫ﺣﯿﺚ‬)
→→→
ν⊥ B,FB(،q:‫ﺷﺤﻨﺔ‬‫ﻛﻮﻟﻮم‬ ‫ﺑﻮﺣﺪة‬ ‫اﻟﺠﺴﯿﻢ‬)C(
ν:‫ﺑﻮﺣﺪة‬ ‫اﻟﺠﺴﯿﻢ‬ ‫ﺳﺮﻋﺔ‬ ‫ﻣﻘﺪار‬)m/sec(.
B:‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫ﻛﺜﺎﻓﺔ‬)‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ﺷﺪة‬ ‫او‬(‫ﺗﺴﻼ‬ ‫ﺑﻮﺣﺪة‬)T(‫ﺣﯿﺚ‬)T=wb/m2
(‫ﺮى‬‫اﺧ‬ ‫ﺪة‬‫وﺣ‬ ‫وھﻨﺎﻟﻚ‬
‫اﻟﻜﺎوس‬ ‫وھﻲ‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫ﻛﺜﺎﻓﺔ‬ ‫ﻟﻘﯿﺎس‬َ)gauss(‫ورﻣﺰه‬)G(‫وان‬)G=10-4
T(
‫ﻟﻠﺘﺤﻮﯾﻞ‬ ‫ﻟﺬﻟﻚ‬‫ﻣﻦ‬:
θ:‫اﻟﺴﺮﻋﺔ‬ ‫ﻣﺘﺠﮫ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺤﺼﻮرة‬ ‫اﻟﺰاوﯾﺔ‬)
→
ν(‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫ﻛﺜﺎﻓﺔ‬ ‫وﻣﺘﺠﮫ‬)
→
B. (
‫ﻣﻼﺣﻈ‬‫ﺎت‬/
1-‫ﻋﻨﺪﻣﺎ‬)
→→
⊥ν B(‫ﻓﺎن‬)θ=90ͦ(‫وان‬)sin90ͦ=1(‫ﯾﺘﺎﺛ‬ ‫ﻟﺬﻟﻚ‬‫اﻟ‬ ‫ﺮ‬‫ﺴﻲ‬‫اﻟﻤﻐﻨﺎطﯿ‬ ‫ﺎل‬‫اﻟﻤﺠ‬ ‫داﺧﻞ‬ ‫واﻟﻤﺘﺤﺮك‬ ‫اﻟﻤﺸﺤﻮن‬ ‫ﺠﺴﯿﻢ‬
‫ﻣﻐﻨﺎطﯿﺴﯿﺔ‬ ‫ﻗﻮة‬ ‫ﺑﺎﻋﻈﻢ‬.
2-‫ﻋﻨﺪﻣﺎ‬‫ﺗﻜﻮن‬)
→
B/ /
→
ν(‫ﻓﺎن‬)θ=0(‫وان‬)sin0=0(‫اﻟﺠﺴ‬ ‫ﯾﺘﺎﺛﺮ‬ ‫ﻻ‬ ‫ﻟﺬﻟﻚ‬‫ﯿ‬‫اﻟﺤﺎﻟﺔ‬ ‫ھﺬه‬ ‫ﻓﻲ‬ ‫ﻣﻐﻨﺎطﯿﺴﯿﺔ‬ ‫ﻗﻮة‬ ‫ﺑﺎﯾﺔ‬ ‫ﻢ‬.
‫ﻣﻼﺣﻈ‬‫ﺎت‬/
1-‫ان‬‫ﻓﻲ‬ ‫اﻟﻤﺆﺛﺮة‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﯿﺔ‬ ‫اﻟﻘﻮة‬‫ﺎه‬‫ﻻﺗﺠ‬ ‫ﺎﻛﺲ‬‫ﻣﻌ‬ ‫ﺎه‬‫ﺑﺎﺗﺠ‬ ‫ﻮن‬‫ﺗﻜ‬ ‫ﺴﻲ‬‫اﻟﻤﻐﻨﺎطﯿ‬ ‫ﺎل‬‫اﻟﻤﺠ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺘﺤﺮﻛﺔ‬ ‫اﻟﺴﺎﻟﺒﺔ‬ ‫اﻟﺸﺤﻨﺔ‬
‫اﻟﻤﻐﻨﺎ‬ ‫اﻟﻘﻮة‬‫اﻟﻤﻮﺟﺒﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺆﺛﺮة‬ ‫طﯿﺴﯿﺔ‬.
2-‫ﺰ‬ ‫اﻟﺮﻣ‬ ‫ﺴﺘﺨﺪم‬ ‫ﯾ‬‫ﻞ‬ ‫ﻣﺜ‬ ‫ﺔ‬ ‫اﻟﻔﯿﺰﯾﺎﺋﯿ‬ ‫ﺔ‬ ‫اﻟﻜﻤﯿ‬ ‫ان‬ ‫ﻰ‬ ‫ﻋﻠ‬ ‫ﺔ‬ ‫ﻟﻠﺪﻻﻟ‬)......F,,B
→→→
ν(‫ﺪاﺧﻞ‬ ‫اﻟ‬ ‫ﻮ‬ ‫ﻧﺤ‬ ‫ﮫ‬ ‫ﻣﺘﺠ‬
)‫اﻟﻨﺎظﺮ‬ ‫ﻋﻦ‬ ‫ﺑﻌﯿﺪا‬(
3-‫اﻟﺮﻣﺰ‬ ‫ﯾﺴﺘﺨﺪم‬‫ﻣﺜﻞ‬ ‫اﻟﻔﯿﺰﯾﺎﺋﯿﺔ‬ ‫اﻟﻜﻤﯿﺔ‬ ‫ان‬ ‫ﻋﻠﻰ‬ ‫ﻟﻠﺪﻻﻟﺔ‬)......F,,B
→→→
ν(‫اﻟﺨﺎرج‬ ‫ﻧﺤﻮ‬ ‫ﻣﺘﺠﮫ‬)‫اﻟﻨﺎظﺮ‬ ‫ﺑﺎﺗﺠﺎه‬(
4-‫ﺎﻟﻘﻮة‬ ‫ﺑ‬ ‫ﺎﺛﺮ‬ ‫ﯾﺘ‬ ‫ﻻ‬ ‫ﺎ‬ ‫ﺑﯿﻨﻤ‬ ‫ﺎ‬ ‫ﻣﺘﺤﺮﻛ‬ ‫او‬ ‫ﺎﻛﻨﺎ‬ ‫ﺳ‬ ‫ﮫ‬ ‫ﻛﻮﻧ‬ ‫ﻦ‬ ‫ﻋ‬ ‫ﺮ‬ ‫اﻟﻨﻈ‬ ‫ﺾ‬ ‫ﺑﻐ‬ ‫ﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿ‬ ‫ﺎﻟﻘﻮة‬ ‫ﺑ‬ ‫ﺎﺛﺮ‬ ‫ﯾﺘ‬ ‫ﺸﺤﻮن‬ ‫اﻟﻤ‬ ‫ﺴﯿﻢ‬ ‫اﻟﺠ‬ ‫ان‬
‫اﻻ‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﯿﺔ‬‫ﻣﺘﺤﺮﻛﺎ‬ ‫ﻛﺎن‬ ‫اذا‬
θν= BSinqFB
EqFE =
)10( 4−
×
)10( 4
×
G T

21. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻧﻲ‬:‫اﻟ‬‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻲ‬ ‫ﺤﺚ‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-22-
5-‫ﺎﺋﻲ‬ ‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬ ‫اﻟﻤﺠ‬ ‫ﺎه‬ ‫اﺗﺠ‬ ‫ان‬)
→
E(‫ﺴﺎﻟﺒﺔ‬ ‫اﻟ‬ ‫ﺸﺤﻨﺔ‬ ‫اﻟ‬ ‫ﺎه‬ ‫ﺑﺎﺗﺠ‬ ‫ﺔ‬ ‫اﻟﻤﻮﺟﺒ‬ ‫ﺸﺤﻨﺔ‬ ‫اﻟ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﻮن‬ ‫ﯾﻜ‬‫ﺎل‬ ‫اﻟﻤﺠ‬ ‫ﻮط‬ ‫ﺧﻄ‬ ‫ﺎ‬ ‫ﺑﯿﻨﻤ‬
‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬)
→
B(‫اﻟﺸﻤﺎﻟﻲ‬ ‫اﻟﻘﻄﺐ‬ ‫ﻣﻦ‬ ‫ﺗﺘﺠﮫ‬)N(‫ﻮﺑﻲ‬‫اﻟﺠﻨ‬ ‫ﺐ‬‫اﻟﻘﻄ‬ ‫اﻟﻰ‬)S(‫ﺎ‬‫دورﺗﮭ‬ ‫ﻞ‬‫ﺗﻜﻤ‬ ‫ﻢ‬‫ﺛ‬ ‫ﺎطﯿﺲ‬‫اﻟﻤﻐﻨ‬ ‫ﺎرج‬‫ﺧ‬‫ﻞ‬‫داﺧ‬
‫اﻟﻤﻐﻨﺎطﯿﺲ‬‫اﻟﺸﻤﺎﻟﻲ‬ ‫اﻟﻘﻄﺐ‬ ‫اﻟﻰ‬ ‫اﻟﺠﻨﻮﺑﻲ‬ ‫اﻟﻘﻄﺐ‬ ‫ﻣﻦ‬.
‫اﻟﺤﺮﻛﻴﺔ‬ ‫اﻟﻜﻬﺮﺑﺎﺋﻴﺔ‬ ‫اﻟﺪاﻓﻌﺔ‬ ‫اﻟﻘﻮة‬)εmotional(:
‫اﻟﺬي‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﮭﺎ‬ ‫وﯾﻘﺼﺪ‬‫ﯾﺘﻮﻟﺪ‬)‫ﯾ‬ُ‫ﺴﺘﺤﺚ‬(‫ﺎل‬‫ﻣﺠ‬ ‫ﻞ‬‫داﺧ‬ ‫ﺴﺎق‬‫اﻟ‬ ‫ﺬه‬‫ھ‬ ‫ﺔ‬‫ﻟﺤﺮﻛ‬ ‫ﺔ‬‫ﻧﺘﯿﺠ‬ ‫ﻠﺔ‬‫ﻣﻮﺻ‬ ‫ﺳﺎق‬ ‫طﺮﻓﻲ‬ ‫ﻋﻠﻰ‬
‫اﻟﻜﮭﺮوﻣﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﺤﺚ‬ ‫ﺣﺎﻻت‬ ‫ﻣﻦ‬ ‫ﺧﺎﺻﺔ‬ ‫ﺣﺎﻟﺔ‬ ‫وﺗﻌﺪ‬ ‫ﻣﻨﺘﻈﻢ‬ ‫ﻣﻐﻨﺎطﯿﺴﻲ‬.
♦‫ﻓ‬‫ﺎ‬‫طﻮﻟﮭ‬ ‫ﻠﺔ‬‫ﻣﻮﺻ‬ ‫ﺎق‬‫ﺳ‬ ‫ﺮك‬‫ﺗﺘﺤ‬ ‫ﺪﻣﺎ‬‫ﻌﻨ‬)l(‫ﺪة‬‫ﺑﻮﺣ‬)m(‫ﺴﺮﻋﺔ‬‫ﺑ‬)ν(‫ﺪة‬‫ﺑﻮﺣ‬)m/sec(‫ﺘﻈﻢ‬‫ﻣﻨ‬ ‫ﺴﻲ‬‫ﻣﻐﻨﺎطﯿ‬ ‫ﺎل‬‫ﻣﺠ‬ ‫ﻲ‬‫ﻓ‬
‫ﻓﯿﻀﮫ‬ ‫ﻛﺜﺎﻓﺔ‬)B(‫ﺗﺴﻼ‬ ‫ﺑﻮﺣﺪة‬)T(‫ﻣﺘﺠﮫ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺰاوﯾﺔ‬ ‫ﺗﻜﻮن‬ ‫ﺑﺤﯿﺚ‬)
→
ν(‫وﻣﺘﺠﮫ‬)
→
B(‫ﺗﺴﺎوي‬)θ(‫ﻋﻠﻰ‬ ‫ﺗﺘﻮﻟﺪ‬ ‫ﻓﺴﻮف‬
‫ﻛﮭﺮﺑﺎﺋﯿﺔ‬ ‫داﻓﻌﺔ‬ ‫ﻗﻮة‬ ‫اﻟﺴﺎق‬ ‫طﺮﻓﻲ‬‫ﻣﺤﺘﺜﺔ‬‫ﺣﺮﻛﯿﺔ‬)εmotional(‫اﻟﺘﺎﻟﯿﺔ‬ ‫ﻟﻠﻌﻼﻗﺔ‬ ‫وﻓﻘﺎ‬ ‫ﺗﻌﻄﻰ‬:
•‫ﻋﻨﺪﻣﺎ‬)
→→
⊥ν B(‫ﻓﺎن‬)°=θ 90(‫وان‬)190sin =°(‫اﻋ‬ ‫ﺗﺘﻮﻟﺪ‬ ‫ﻟﺬﻟﻚ‬‫ﺣﺮﻛﯿﺔ‬ ‫ﻣﺤﺘﺜﺔ‬ ‫ﻛﮭﺮﺑﺎﺋﯿﺔ‬ ‫داﻓﻌﺔ‬ ‫ﻗﻮة‬ ‫ﻈﻢ‬.
•‫ﻋﻨﺪﻣﺎ‬)
→
B/ /
→
ν(‫ﻓﺎن‬)θ=0(‫وان‬)sin0=0(‫ﺗﺘﻮﻟﺪ‬ ‫ﻻ‬ ‫ﻟﺬﻟﻚ‬)εmotional(‫اﻟﺴﺎق‬ ‫طﺮﻓﻲ‬ ‫ﻋﻠﻰ‬.
•‫ﺪاﺋﺮة‬ ‫ﻟﻠ‬ ‫ﺔ‬ ‫اﻟﻜﻠﯿ‬ ‫ﺔ‬ ‫اﻟﻤﻘﺎوﻣ‬ ‫ﻮن‬ ‫ﺗﻜ‬ ‫ﺚ‬ ‫ﺑﺤﯿ‬ ‫ﺔ‬ ‫ﻣﻘﻔﻠ‬ ‫ﺔ‬ ‫ﻛﮭﺮﺑﺎﺋﯿ‬ ‫ﺮة‬ ‫داﺋ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﺰء‬ ‫ﺟ‬ ‫ﻠﺔ‬ ‫اﻟﻤﻮﺻ‬ ‫ﺴﺎق‬ ‫اﻟ‬ ‫ﻮن‬ ‫ﺗﻜ‬ ‫ﺪﻣﺎ‬ ‫وﻋﻨ‬)R(‫ﺚ‬ ‫ﺣﯿ‬
)R‫اﻟﺮﺑﻂ‬ ‫واﺳﻼك‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﺗﻤﺜﻞ‬(‫ﺎﻧﻮن‬‫ﻟﻘ‬ ‫ﺎ‬‫وﻓﻘ‬ ‫ﺴﺐ‬‫ﯾﺤ‬ ‫ﺪاﺋﺮة‬‫اﻟ‬ ‫ﺬه‬‫ھ‬ ‫ﻓﻲ‬ ‫ﻣﺤﺘﺚ‬ ‫ﺗﯿﺎر‬ ‫ﯾﻨﺴﺎب‬ ‫ﺳﻮف‬ ‫ﻟﺬﻟﻚ‬
‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫اوم‬:
•‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻓﻲ‬ ‫اﻟﻀﺎﺋﻌﺔ‬ ‫او‬ ‫ﺪدة‬ ‫اﻟﻤﺘ‬ ‫اﻟﻘﺪرة‬ ‫اﻣﺎ‬)Pdissipated(‫اﻟ‬ ‫ﺔ‬‫اﻟﻤﻘﺎوﻣ‬ ‫ﻓﻲ‬ ‫ﺣﺮارة‬ ‫ﺑﮭﯿﺌﺔ‬ ‫ﺗﻈﮭﺮ‬ ‫واﻟﺘﻲ‬‫ﺔ‬‫ﻜﻠﯿ‬)R(
‫ﻟﻠﻌﻼﻗﺎت‬ ‫وﻓﻘﺎ‬ ‫ﻓﺘﺤﺴﺐ‬‫اﻻﺗﯿﺔ‬:
‫اﻟﻮاط‬ ‫ھﻲ‬ ‫اﻟﻤﺘﺒﺪدة‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫اﻟﻘﺪرة‬ ‫ﻗﯿﺎس‬ ‫وﺣﺪة‬ ‫ﺣﯿﺚ‬)Watt(‫ﻟﮫ‬ ‫وﯾﺮﻣﺰ‬)W. (
•‫ﺛﺎﻧﯿﺔ‬ ‫ﻣﻐﻨﺎطﯿﺴﯿﺔ‬ ‫ﻗﻮة‬ ‫ﺗﺘﻮﻟﺪ‬ ‫ﺳﻮف‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻓﻲ‬ ‫ﻛﮭﺮﺑﺎﺋﻲ‬ ‫ﺗﯿﺎر‬ ‫ﻟﻤﺮور‬ ‫وﻧﺘﯿﺠﺔ‬)FB2(‫ﺎه‬‫وﺑﺎﺗﺠ‬ ‫اﻟﺴﺎق‬ ‫ﻋﻠﻰ‬ ‫ﻋﻤﻮدﯾﺔ‬ ‫وﺗﻜﻮن‬
‫ﻻﺗﺠ‬ ‫ﺎﻛﺲ‬‫ﻣﻌ‬‫ﺔ‬‫ﻣﺘﺒﺎطﺌ‬ ‫ﺔ‬‫اﻟﺤﺮﻛ‬ ‫ﻞ‬‫وﺗﺠﻌ‬ ‫ﺴﺎق‬‫اﻟ‬ ‫ﺔ‬‫ﺣﺮﻛ‬ ‫ﺔ‬‫ﻋﺮﻗﻠ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﻞ‬‫ﺗﻌﻤ‬ ‫ﺬﻟﻚ‬‫ﻟ‬ ‫ﻰ‬‫اﻟﯿﻤﻨ‬ ‫ﻒ‬‫اﻟﻜ‬ ‫ﺪة‬‫ﻗﺎﻋ‬ ‫ﺴﺐ‬‫ﺣ‬ ‫ﺔ‬‫اﻟﺤﺮﻛ‬ ‫ﺎه‬
)‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﻏﯿﺮ‬(‫اﻟﺘﺎﻟﯿﺔ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﻣﻦ‬ ‫اﻟﺜﺎﻧﯿﺔ‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﯿﺔ‬ ‫اﻟﻘﻮة‬ ‫وﺗﺤﺴﺐ‬:
•‫ﺔ‬ ‫ﺧﺎرﺟﯿ‬ ‫ﻮة‬ ‫ﻗ‬ ‫ﺴﻠﯿﻂ‬ ‫ﺗ‬ ‫ﺐ‬ ‫ﯾﺘﻄﻠ‬ ‫ﺔ‬ ‫ﺛﺎﺑﺘ‬ ‫ﺴﺮﻋﺔ‬ ‫ﺑ‬ ‫ﺮك‬ ‫ﺗﺘﺤ‬ ‫ﺴﺎق‬ ‫اﻟ‬ ‫ﻞ‬ ‫ﻧﺠﻌ‬ ‫ﻲ‬ ‫وﻟﻜ‬)Fpull(‫اﻟ‬ ‫ﺴﺤﺐ‬ ‫ﺗ‬‫ﻮة‬ ‫اﻟﻘ‬ ‫ﺴﺎوي‬ ‫ﺗ‬ ‫ﻲ‬ ‫وھ‬ ‫ﺴﺎق‬
‫ان‬ ‫أي‬ ‫اﺗﺠﺎھﺎ‬ ‫وﺗﻌﺎﻛﺴﮭﺎ‬ ‫ﻣﻘﺪارا‬ ‫اﻟﺜﺎﻧﯿﺔ‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﯿﺔ‬:
2Bpull FF =
lBIF 2B =
R
B
Ior
R
I ind
motional
ind
lν
=
ε
=
R
PorIPorR.IP
2
motional
dissipatedmotionaldissipated
2
dissipated
ε
=ε==
θν=ε sinBmotional l