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CURRENT ELECTRICITY - II
1. Kirchhoff’s Laws of electricity
2. Wheatstone Bridge
3. Metre Bridge
4. Potentiometer
i) Principle
ii) Comparison of emf of primary cells
Created by C. Mani, Principal, K V No.1, AFS, Jalahalli West, Bangalore
KIRCHHOFF’S LAWS:
I Law or Current Law or Junction Rule:
The algebraic sum of electric currents at a junction in any
electrical network is always zero.
O
I1
I4
I2
I3
I5
I1 - I2 - I3 + I4 - I5 = 0
Sign Conventions:
1. The incoming currents towards the junction are taken positive.
2. The outgoing currents away from the junction are taken negative.
Note: The charges cannot accumulate at a junction. The number
of charges that arrive at a junction in a given time must leave in
the same time in accordance with conservation of charges.
II Law or Voltage Law or Loop Rule:
The algebraic sum of all the potential drops and emf’s along any
closed path in an electrical network is always zero.
Sign Conventions:
1. The emf is taken negative when we traverse from positive to negative
terminal of the cell through the electrolyte.
2. The emf is taken positive when we traverse from negative to positive
terminal of the cell through the electrolyte.
The potential falls along the direction of current in a current path
and it rises along the direction opposite to the current path.
3. The potential fall is taken negative.
4. The potential rise is taken positive.
Loop ABCA:
- E1 + I1.R1 + (I1 + I2).R2 = 0
E1
R1
E2
R3
R2
I1
I2
I1
I2
I1
I2 I1 + I2
A B
C
D
Note: The path can be traversed
in clockwise or anticlockwise
direction of the loop.
Loop ACDA:
- (I1 + I2).R2 - I2.R3 + E2 = 0
Wheatstone Bridge:
I1
I
Ig
I1 - Ig
I - I1
E
A
B
C
D
P Q
R S
G
I
I
I
I - I1 + Ig
Loop ABDA:
-I1.P - Ig.G + (I - I1).R = 0
Currents through the arms are assumed by
applying Kirchhoff’s Junction Rule.
Applying Kirchhoff’s Loop Rule for:
When Ig = 0, the bridge is said to balanced.
By manipulating the above equations, we get
Loop BCDB:
- (I1 - Ig).Q + (I - I1 + Ig).S + Ig.G = 0
P
Q
R
S
Metre Bridge:
A B
R.B (R) X
G
J
K
E
l cm 100 - l cm
Metre Bridge is based
on the principle of
Wheatstone Bridge.
When the galvanometer
current is made zero by
adjusting the jockey
position on the metre-
bridge wire for the given
values of known and
unknown resistances,
R RAJ
X RJB
R AJ
X JB
R l
X 100 - l
(Since,
Resistance α
length)
Therefore, X = R (100 – l) ∕ l
Potentiometer:
J
V
+
K
E
A
Rh
+
l cm
I
Principle:
V = I R
= I ρl/A
If the constant current flows
through the potentiometer wire
of uniform cross sectional area
(A) and uniform composition
of material (ρ), then
V = Kl or V α l
0
l
V
V /l is a constant.
The potential difference across any length of a wire
of uniform cross-section and uniform composition is
proportional to its length when a constant current
flows through it.
A
B
100
200
300
400
0
+
E1
E2
+
R.B
G
J1
l1
J2
l2
E
A
K
A
B
Rh
+
I
100
200
300
400
0
Comparison of emf’s using
Potentiometer:
The balance point is
obtained for the cell when
the potential at a point on
the potentiometer wire is
equal and opposite to the
emf of the cell.
E1 = VAJ1
= I ρl1 /A
E2 = VAJ2
= I ρl2 /A
E1 / E2 = l1 /l2
Note:
The balance point will not be obtained on the potentiometer wire if the fall
of potential along the potentiometer wire is less than the emf of the cell to
be measured.
The working of the potentiometer is based on null deflection method. So
the resistance of the wire becomes infinite. Thus potentiometer can be
regarded as an ideal voltmeter.
End of Current Electricity

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2_current_electricity_2 - Copy.pptx

  • 1. CURRENT ELECTRICITY - II 1. Kirchhoff’s Laws of electricity 2. Wheatstone Bridge 3. Metre Bridge 4. Potentiometer i) Principle ii) Comparison of emf of primary cells Created by C. Mani, Principal, K V No.1, AFS, Jalahalli West, Bangalore
  • 2. KIRCHHOFF’S LAWS: I Law or Current Law or Junction Rule: The algebraic sum of electric currents at a junction in any electrical network is always zero. O I1 I4 I2 I3 I5 I1 - I2 - I3 + I4 - I5 = 0 Sign Conventions: 1. The incoming currents towards the junction are taken positive. 2. The outgoing currents away from the junction are taken negative. Note: The charges cannot accumulate at a junction. The number of charges that arrive at a junction in a given time must leave in the same time in accordance with conservation of charges.
  • 3. II Law or Voltage Law or Loop Rule: The algebraic sum of all the potential drops and emf’s along any closed path in an electrical network is always zero. Sign Conventions: 1. The emf is taken negative when we traverse from positive to negative terminal of the cell through the electrolyte. 2. The emf is taken positive when we traverse from negative to positive terminal of the cell through the electrolyte. The potential falls along the direction of current in a current path and it rises along the direction opposite to the current path. 3. The potential fall is taken negative. 4. The potential rise is taken positive. Loop ABCA: - E1 + I1.R1 + (I1 + I2).R2 = 0 E1 R1 E2 R3 R2 I1 I2 I1 I2 I1 I2 I1 + I2 A B C D Note: The path can be traversed in clockwise or anticlockwise direction of the loop. Loop ACDA: - (I1 + I2).R2 - I2.R3 + E2 = 0
  • 4. Wheatstone Bridge: I1 I Ig I1 - Ig I - I1 E A B C D P Q R S G I I I I - I1 + Ig Loop ABDA: -I1.P - Ig.G + (I - I1).R = 0 Currents through the arms are assumed by applying Kirchhoff’s Junction Rule. Applying Kirchhoff’s Loop Rule for: When Ig = 0, the bridge is said to balanced. By manipulating the above equations, we get Loop BCDB: - (I1 - Ig).Q + (I - I1 + Ig).S + Ig.G = 0 P Q R S
  • 5. Metre Bridge: A B R.B (R) X G J K E l cm 100 - l cm Metre Bridge is based on the principle of Wheatstone Bridge. When the galvanometer current is made zero by adjusting the jockey position on the metre- bridge wire for the given values of known and unknown resistances, R RAJ X RJB R AJ X JB R l X 100 - l (Since, Resistance α length) Therefore, X = R (100 – l) ∕ l
  • 6. Potentiometer: J V + K E A Rh + l cm I Principle: V = I R = I ρl/A If the constant current flows through the potentiometer wire of uniform cross sectional area (A) and uniform composition of material (ρ), then V = Kl or V α l 0 l V V /l is a constant. The potential difference across any length of a wire of uniform cross-section and uniform composition is proportional to its length when a constant current flows through it. A B 100 200 300 400 0
  • 7. + E1 E2 + R.B G J1 l1 J2 l2 E A K A B Rh + I 100 200 300 400 0 Comparison of emf’s using Potentiometer: The balance point is obtained for the cell when the potential at a point on the potentiometer wire is equal and opposite to the emf of the cell. E1 = VAJ1 = I ρl1 /A E2 = VAJ2 = I ρl2 /A E1 / E2 = l1 /l2 Note: The balance point will not be obtained on the potentiometer wire if the fall of potential along the potentiometer wire is less than the emf of the cell to be measured. The working of the potentiometer is based on null deflection method. So the resistance of the wire becomes infinite. Thus potentiometer can be regarded as an ideal voltmeter. End of Current Electricity