Laboratory session in Physics II subject for September 2016-January 2017 semester in Yachay Tech University (Ecuador). Topic covered: electricity, electrical circuits, resistances, capacitances, diodes Based on Bruna Regalado's work

1. GUIDE FOR PRACTICE 3:
LAWS OF KIRCHHOFF, RC CIRCUITS AND DIODES
1. CONTENT:
Kirchhoff’ laws
First and Second Law of Kirchhoff
RCCircuits
Loading and unloading of a condenser
Diodes
Definition, Types and Uses
LEARNING OBJECTIVES:
1-.)Knowing Ohm’s law and Kirchhoff’s laws.
2-.)Get the equations theoretically current and voltage in the loading and discharge of a
capacitor.
3-.)Experimentally demonstrate the loading and discharge of a capacitor.
4-.)Combine diodes and transistors in an electronic circuit.
2. THEORETICAL BASICS:
Mesh analysis in electrical circuits
Before beginning this is appropriate to provide some definitions of interest:
Node: point between three or more elements. In Figure 1, the nodes are the points 1 and 2.
Branch: element or set of elements between two nodes. In Figure 1, between points 1 and 2
there are two branches, containing only one resistor and the other contains two resistors and a
coil.
Mesh: set of branches forming a closed line and contains other inside. In Figure 1 in the closed
line beginning at point 1, it contains the two branches mentioned before and returns to the same
point.
Figure 1: Electrical circuit
Kirchhoff's laws are:
• First Kirchhoff's law: the algebraic sum of the currents of a node must be zero at any instant
of time. This means that the sum of the currents entering the node is equal to the sum of the
currents leaving that node. Note Figure 2.
In a closed circuit
Figure 2: Law of nodes Figure 3: Law of mesh
PHYSICS
LABORATORY II

2. • Second Kirchhoff's law (Figure 3): the algebraic sum of the potential drops (voltages) in a
closed mesh must be zero at any instant of time online. This means that the sum of the tensions
in one direction is equal to the sum of the voltages in the opposite direction.
To perform the analysis of the signs is considered:
• The passive elements (which consume or absorb power) have the voltage and electric current in
the same direction. These are capacitors, resistors and inductors.
• The active elements (electric power sagging) have the voltage and electric current have
opposite direction. These are for example the voltage generators and power sources or batteries.
In mesh analysis must follow a series of steps that will arrive at the values of electric currents
and potential drops in each mesh:
1- Each mesh a stream so that all have the same direction is assigned. For example in Figure 2
can be seen the currents I1, I2 and I3.
2- Currents external branches (belonging to a single mesh) will mesh current.
3- Currents internal branches (belonging to two screens) is the difference of two mesh currents.
4- Finally, it is solving the system of equations which will have as many equations as unknowns
currents.
RC circuits:
Circuits direct current (DC or DC) containing capacitors (condensers), the current is always in the
same direction but may vary over time. An RC circuit is one which is formed by a resistor and a
capacitor in series.
Charging a capacitor:
Suppose the capacitor circuit shown in Figure 4 is initially uncharged therefore not be a current
while the switch S is open. However, if the switch is closed at t = 0, the load will begin to flow,
establishing a current in the circuit, and the capacitor will begin charging. During this process, the
charges do not jump from one plate to another capacitor. Instead, the load is transferred from one
plate to another and their connecting wires due to the electric field battery set conductors (wires),
until the capacitor is fully charged. As the capacitor charges the potential difference increases. The
value of the maximum load on the plates depend on the source voltage. Once the maximum load is
reached, the current in the circuit is zero, since the potential difference applied to the capacitor is
equal to that supplied by the source (Vi).
Figure 4: RC circuits
If the circuit of Figure 4 for an instant after the switch is closed and applying the laws of
Kirchhoff runs you can be obtained equations charge and current as follows:
Vi-Vc-VR = 0 (2nd Law of Kirchhoff)
Where: Vi = voltage source; Vc: voltage at the capacitor; VR: Voltage resistance the following
equations are established:
− − = 0 Knowing that I= y
that =
− − = 0 = −

3. −
=
−
= −
−
=
Solving differential equations has the
right equation:
−
= −
It has integrand:
( − )
= −
Solvingthe integral:
−
−
= −
The capacitor charging
equation is obtained:
( ) = (1 − )
(Figure 5)
If desired to obtain the equation of voltage on
the capacitor is divided q(t)/C=Vc(t):
!(") = #($ − % " &'⁄
)
Differentiating the equation q(t) the equation of the
load current is obtained:
)(") = #
&
% "/&'
(Figure 6)
The time it takes the voltage on the capacitor (Vc) to go from 0 volts to 63.2% of the supply
voltage is given by the formula: τ=RC. Where the resistor R is in ohms, the capacitor C in
milifaradios and the result will be in milliseconds. After 5τ the voltage has risen to 99.3% of its
final value. The value of τ is called: TIME CONSTANT
Figure 5: Charging curve of a capacitor Figure 6: Current curve versus time
Discharge of a capacitor:
When a capacitor is charged and you want to download very quickly enough to make a short
circuit between its terminals. This operation consists of putting between them a thread of very
little resistance. If one wishes to discharge the capacitor slowly, then across its terminals a
resistor is placed. Turning off the power capacitor start to discharge and voltage in will decrease.
The current will have an initial value of Vi/R and decrease until it reaches 0. The discharge time
depends on the value of the resistor R, the capacitor C and voltage exists in the capacitor at the
initial moment of discharge. The potential difference between the ends of the capacitor decreases
with time t following an exponential law. When the switch is open there is a potential difference
Q / C applied to the capacitor and a potential difference equal to zero applied to the resistor,
since I = 0. Considering these claims the following equations applied to the circuit of Figure 4
are obtained:
Figure 7: Discharge circuit of a capacitor
ApplyingKirchhoff’s 2nd Law:
− − + = 0 − − = 0 − − = 0 = −

4. Integrating:
= −
1
,
Solvingtheintegrall:
-
= −
( ) = - +.⁄
Q: Initial charge on the
capacitor
( ) = −
- /+.
Note: the sign (-) in the current equation indicates that as the capacitor discharges, the current
direction is in the opposite direction when it was charging.
Figure 8: Discharge curve of a Capacitor Figure 9: Current curve versus time
Semiconductor diode:
The semiconductor diode is the simplest semiconductor device and can find virtually any
electronic circuit. The diodes are manufactured in versions silicon (the most used) and
germanium.
Figure 10: Diodes
Seeing the diode symbol in Figure 10 shows: A (anode), K (cathode).
The diodes consist of two parts, one called N and the other called P,
separated by a barrier or bonding joint call. This barrier or junction is
0.3 volts in the germanium diode approximately 0.6 volts and the
silicon diode.
Principle of operation of a diode:
The N-type semiconductor having free electrons (electron excess) and the P-type semiconductor
has free holes (absence or lack of electrons). When a positive voltage is applied to the P side and
a negative side N, the electrons in the N side are pushed next P and electrons flow through the
material P beyond the boundaries of the semiconductor. Likewise the holes in the material P are
pushed with a negative voltage side of the material N and holes flow through the material N. In
the opposite case, when a positive voltage is applied to the N side and a negative side P,
electrons in the N side are pushed next N and P side holes are pushed next P. in this case the
electrons in the semiconductor are not moving and therefore no current. The diode can be made
to work in 2 different ways (figure 11):
1-.)Forward bias
It is when the current through the diode follows the path of the arrow (the diode), or the anode to
cathode. In this case the current through the diode very easily behaving almost like a short circuit
2-.)Reverse bias
It is when the diode current desired circular direction opposite to arrow (arrow of the diode), or
from cathode to anode direction. In this case no current through the diode, and practically
behaves like an open circuit.
Note: The above operation relates to ideal diode, this means that the diode is taken as a perfect
element (as is done in most cases), both in forward bias and reverse bias.

5. Figure 11: Diode characteristic curve
Specifications diodes:
PIV: Peak Inverse or Inverse Voltage Peak Reverse Voltage or Rupture: The maximum peak
voltage or AC that can be applied to a diode when it is reverse biased.
=Forward Current: The maximum current (AC / DC) flowing through the diode when
forward biased.
=Forward Voltage Drop: This is the voltage drop produced by the internal resistance
of the diode when forward biased
=Reverse Leakage current: Is flowing through the diode when it is reverse biased.
=Rupture voltage or breakdown voltage: The maximum voltage is applied to the diode should
not to damage so either directly or reverse bias.
3. LABORATORY MATERIALS:
Panel pins 4 mm
Multimeter
Diode Si-1N4007
Connecting lines (cable)
Resistance 47Ω, 1W, G1
Switch, G1
Resistance 100 Ω, 1W, G1
Resistance 1k Ω, 1W, G1
Graphite resistance 4.7 kΩ, 1W, G1
Resistance 47 kΩ, 1W, G1
Resistance 470Ω, 1W, G1
Resistance 10 KΩ, 1W, G1
Power supply DC de 0 a 12V, 2A/AC: 6V, 12V,
5A
Electrolytic capacitors 470 µF, 16V
Stopwatch
4. EXPERIENCES:
Activity 1: Implementation and verification of Kirchhoff's laws in the resolution of an
electrical circuit
1) Applying Kirchhoff's laws for the theoretical values: voltage and current.
2.) Connect the circuit shown in figure.

6. VS= 9V
R1= 10KΩ
R2= 4,7KΩ
Ra= 100Ω
Rb= 1KΩ
3.) With the Meter measures the voltage values in every part of the electrical circuit.
4.) By Ohm's Law to determine the value of the currents flowing through the circuit
Activity 2: Demonstration of the charging process of a capacitor in an RC circuit
1-.)Build the circuit shown in the figure, according to the instructions given by the teacher. Pass
theswitch and startchargingthe capacitor.
Where:
R=10KΩ
C=470µF
Vi=10V
2-.)Evaluate the voltage equations (Vc) and current I(t) for each value of τ and write the
corresponding equation.
Activity 3: Demonstration of the process of discharge of a capacitor in an RC circuit
At the end of measurements charging process proceeds to the discharge process, for which the
circuit is used in the current conditions by following these steps.
1-.) Remove only one end of the voltmeter (to avoid capacitor discharge).
2.) Place the switch in off position.
3-.) Turn off the power and remove, replace at its terminals for cable.
4.) Connect the cable disconnected from the meter before and immediately pass the switch to on
and start once experimental measurements capacitor discharge.
Activity 4: Verification of the characteristic curve of a diode
1.)Perform the assembly shown in Figure (forward bias). Place the meter at the ends of the
diode. To set the value of supply voltage measured with multimeter.

7. 2.) Apply the 2nd Law of Kirchhoff and get the equation that represents the diode current (i
3.) Assemble the circuit but again reverse bias (reverse the polarity of the source)
NOTE: VD=Vi ∀Vi<0.65 and V
data).
WARNING: Working with Vi values between (
of damaging the diode.
5. DATA EVALUATION
ACTIVITY 1
Complete the following tables:
VS VRaTeór. VRaExp.
9V
ItTeór. ItExp.
ACTIVITY 2
a-.)Complete the following tables
Value of0 Equation ofVc
t=RC=1 0
t=2RC=2 0
t=3RC=3 0
t=4RC=4 0
b-.) Perform the following graphs Loading and unloading
t(s) Vexp(V) Vteórico(V)
2
5
10
15
20
Where:
Vi<5V y Vi<(
R=47Ω
2.) Apply the 2nd Law of Kirchhoff and get the equation that represents the diode current (i
.) Assemble the circuit but again reverse bias (reverse the polarity of the source)
<0.65 and VD≅Vi∀Vi ≥0,65; Vf = 0.93 (forward voltage, manufacturer's
Working with Vi values between (-5V and 5V, if it exceeds these
VRbTeór. VRbExp. VR1Teór. VR1Exp. VR2Teór.
Exp. I1 Teór. I1Exp. I2 Teór. I2Teór.
Complete the following tables:
Vc (theoric value) Equation of I(t)
Perform the following graphs Loading and unloading: Vexpc vs t(s); I(t) vs t(s).
Error
t(s): is the time taken with
the stopwatch
Vi<5V y Vi<(-5V)
Ω
2.) Apply the 2nd Law of Kirchhoff and get the equation that represents the diode current (iD).
.) Assemble the circuit but again reverse bias (reverse the polarity of the source)
Vf = 0.93 (forward voltage, manufacturer's
5V and 5V, if it exceeds these values is a risk
Teór. VR2Exp.
vs t(s).
taken with

8. ACTIVITY 3
a-.) Complete the following tables:
Value of 0 Equation of Vc (theoric value) Equation of I(t)
t=RC=1 0
t=2RC=2 0
t=3RC=3 0
t=4RC=4 0
b-.) Perform the following graphs Loading and unloading: Vexpc vs t(s); I(t) vs t(s).
c-.) According the second table, obtain the time constant τ by the slope in a linear regression
involving Vexp(V) and t(s). Do NOT forget the linearization of the formula!
ACTIVITY 4
a-.)Complete the following tables:
Forward bias
Reverse bias
b-.) Construct the characteristic curve (experimental) with the data, representing the forward bias
and reverse.
Specific questions
1-.) Do you think that equilibrium conditions are established in an electrical circuit using
Kirchhoff's laws? Justify your answer.
2-.) For what purpose resistance in the RC circuit is used?
3-.) What kind of systems are the RC circuit?
4-.) What determines the current in an RC circuit during the download process?
5-.) When you start driving through the diode?
6-.) The graphs obtained diode, indicate when the current flow is blocked?
t(s) Vexp(V) Vteórico(V) Error
2
5
10
15
20
Vi (V) VD iD
0
0,25
0,50
0,65
1,00
2,00
5,00
Vi (V) VD iD
0
-1,00
-2,00
-4,00
-5,00

9. 5-. EXTRA HELP LITERATURE
• Jerry D. Wilson, Anthony J. Buffa and Bo Lou. Physical. Pearson Prentice Hall, 2007
• Paul A. Tipler and Gene Mosca. Physics for Science and Technology, 10th edition Editorial
Reverte, 2007
• Paul G. Hewitt. Conceptual Physics, 11th edition. Pearson Education, 2009
• Raymond A. and C. VuilleSerway. College physics. Cengage Learning, 2011
• Richard P. Feynman, Robert B. Leighton, and Matthew L. Sands. The Feynman Lectures on
Physics "vol. 1. Addison Wesley, 1989
Links:
Charging and discharging of a capacitor
https://www.youtube.com/watch?v=eKhB11jPZyM
Capacitors
https://www.youtube.com/watch?v=EkUIUSZtdU0
Capacitor
https://www.youtube.com/watch?v=YDXWACqLnmo
Charging and discharging of a capacitor
https://www.youtube.com/watch?v=C5lWplbeU3M