Kirchhoff's voltage law states that the sum of the voltages around any closed loop in a circuit must be zero. It provides a way to analyze the voltages in electric circuits. The document explains Kirchhoff's voltage law and how it can be applied to determine the voltages across individual components in both series and parallel circuits. Examples are also provided to demonstrate how to use the law to solve for unknown voltages.

1. Kirchhoff's Voltage Law
By
Dr. Arroj Ahmad Khan

2. Basic Laws
To actually determine the values of variables voltage,
current and power in an electric circuit requires that we
understand some fundamental laws that govern the
electric circuits. These laws known as Ohm's law and
Kirchhoff's laws upon which electric circuit analysis is
built.

3. Ohm's Law
 Resistance
The physical property, or ability to resist current, is known as
resistance.
Materials in general have a characteristic behavior of resisting
the flow of electric charge. The resistance of any material with
a uniform cross-sectional area A depends on A and its length
l. In mathematical form,
roh is the resistivity of the material in ohm-meter.

4. Ohm's law stated as,
“The current I through a conductor between two points is directly
proportional to the voltage V across the two points.”
Mathematically,
R is proportionality constant
A circuit with R=0 is called a short
circuit, as shown in fig. For a short
circuit
Current could be any value.

5. For the circuit shown, calculate the voltage
v ,
Example

6. Series Circuits
A circuit consists of any number of elements joined at terminal
points, providing at least one closed path through which charge
can flow
Or
A circuit composed solely of components connected in series is
known series circuit.
Fig. has three elements joined at three
terminal points, (a,b and c) to provide a
closed path for the current I.

7. In this fig. the resistors R1 and R2 are in series because they
have only point b in common. The other ends of the resistors are
connected elsewhere in the circuit. For the same reason, the
battery E and resistor R1 are in series (terminal a in common),
and the resistor R2 and the battery E are in series (terminal c in
common). Since all the elements are in series, the network is
called a series circuit.

8. Two common examples of series connections include the tying of
small pieces of rope together to form a longer rope and the
connecting of pipes to get water from one point to another.
If the circuit of figure is modified such that a current carring
resistor R3 is introduced as shown below, the resistors R1 and R2
are no longer in series due to violation of number 2 of the above
definition of series elements
 The current is the same through
series elements.
 The total resistance of a series
circuit is the sum of all resistances.

9. In general, to find the total resistance of N resistors in series, the
following equation is applied.
Once the total resistance is known, the circuit of figure can be
redrawn as,
The current drawn can be determined
using Ohm's law, as follows

10. The fact that the current is the same through each element of
initial fig. permits a direct calculation of the voltage across each
resistor using Ohm's law; that is,
Example

11. Solution

12. Example
Solution

13. Kirchhoff's Voltage Law
A closed loop is any continuous path that leaves a point in one
direction and returns to that same point from another direction
without leaving the circuit.
In the figure by following the current, we
can trace a continuous path that leaves
point a through R1 and returns through E
without leaving the circuit. Therefore,
abcda is a closed loop.

14. We can apply the KVL either on clockwise or anticlockwise we get
the same result.
A plus sign is assigned to a potential rise (- to +), and a minus sign
to a potential drop (+ to -). If we follow the current in figure from
point a, we first encounter a potential drop V1 (+ to -) across R1
and then another potential drop V2 across R2. Continuing through
the voltage source, we have a potential rise E (- to +) before
returning to point a.
Closed loop, and V the potential drops and rises, we have