ELCT708: Electronics for
Biotechnology
Lab Report 2
Name: -------------------------------------------------Group: --------------------------------------------------
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KVL & KCL
Objective:
The objective of the experiments in this LAB session is to verify Kirchoff’s
Voltage Law (KVL) and Kirchoff’s Current Law (KCL) and to verify also the
voltage divider and current divider relations which arise due to serial and parallel
configurations of resistors.
Introduction:
I. KVL:
Consider a circuit in which three resistors R1, R2 and R3 are connected in
Series as shown in the following figure:
Figure 1
The total resistance of this set of resistors connected in series (in this case
three), is the sum of the resistances of the individual resistors:
The current, I, flows through each of the resistors. The total resistance
between the points A and B, call it R, will produce a potential drop V between the
test points, where V = IR.
The potential difference between each of the individual resistors will be the
total potential drop between A and B will be the sum of the individual potential
drops across each resistor. Thus,
V= V +V +V
1
2
2
3
This is what is called Kirchoff’s Voltage Law (KVL), which states
that:
“The sum of voltage drops around a closed path must equal to zero”
Due to serial configuration the voltage V is divided between the three resistors,
where the value of voltage across each resistor can be calculated as follows:
V = V R / (Σ R)
1
1
V = V R / (Σ R)
2
2
V = V R / (Σ R)
3
This is what is called Voltage
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Divider Rule.
II. KCL:
Consider a circuit in which three resistors R1, R2 and R3 are connected in
Parallel as shown in the following figure:
Figure 2
Thus the total resistance of a set of resistors connected in parallel (in this case
three) is given by the equation:
At the point A, the current, I, divides into three smaller currents I1, I2, and I3, in
such a way that the total current is given by:
I = I1 + I2 + I3
3
This is what is called Kirchoff’s
Current Law (KCL) which states that:
“The sum of currents leaving or entering a node must equal zero”
The potential difference across the points A and B will be V, and will be
equal to the current I multiplied by the total resistance of the parallel resistors, R.
V = IR.
Since each resistor is connected across the same points A and B, the
potential difference across each is the same, namely, V. The currents through
each resistor in turn will be I1 = V/R1, I2 = V/R2 and I3 = V/R3.
If we have two resistors, R and R , connected in parallel, where R is their parallel
1
2
equivalence, the total current I will be divided between the resistors, where the
value of the current flowing through each resistor can be calculated by the
following relations:
I = I R / (Σ R)
1
2
I = I R1 / (Σ R)
2
This is what is called Current
Divider Rule.
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Question (1):
From the KVL and KCL experiment:
a) KVL:
V1=……… V (from voltage divider rule)
V1=……… V (measured)
V2=……… V (from voltage divider rule)
V2=……… V (measured)
V3=……… V (from voltage divider rule)
V3=……… V (measured)
V1+V2+ V3=……. V (measured)
b) KCL:
Itotal=………A (Calculated)
I1=……… A (from current divider rule)
I1=……… A (measured)
I2=……… A (from current divider rule)
I2=……… A (measured)
I3=……… A (from current divider rule)
I3=……… A (measured)
I1+ I2+I3=……. A (measured)
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Question (2):
R2
R6
5K
100
R1
R4
R5
R7
500
1k
1k
100
VT
R3
200
5 Vdc
R8
200
a) Using Voltage source of value 5V:
R1
R2
R3
R4
R5
R6
R7
R8
V
I
b) Comment on the values of the currents passing through R4 and R5
c) Comment on the values of the Voltages across R1 and R2.
d) Comment on the value of the current passing through R5 against the values
of the currents passing through R6, R7 and R8.
e) Comment on the values of the voltages across R6, R7 and R8
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