Page 120 - Basic Electrical Engineering

a positive sign may be assigned to the rise in voltage and a negative sign may
be assigned to the fall or drop in voltage.
KVL can be expressed mathematically as

where V represents the voltages of all the branches in a mesh or a loop, i.e.,
j
in the jth element around the closed loop having n elements.

Let us apply KCL and KVL in a circuit shown in Fig. 2.20 (b). The current
flowing through the branches have been shown.
Applying KCL at node B, we can write

I + I = I (i)
2
3
1
Now, let us apply KVL in mesh ABEFA and mesh CBEDC, respectively.
For the mesh ABEFA, starting from point A, the sum of voltage drops and

voltage rise are equated to zero as

+ I R − I R − E = 0
1
3
1
1
3
or, I R − (I − I ) R − E = 0 (ii)
2
1
3
1
1
1
The students need to note that while we move in the direction of the flow of
current, the voltage across the circuit element is taken as negative. While we
move from the negative terminal of the source of EMF to the positive
terminal, the voltage is taken as positive. That is why we had taken voltage
drop across the branch AB as + I R and across BE as −I R . Since we were
1 1
3 3
moving from the positive terminal of the battery towards its negative terminal
while going round the mesh we had considered it as voltage drop and

assigned a negative sign.
Using this convention, for the mesh CBEDC, applying KVL we can write

− I R − I R − E = 0
1
1
3
2
3