Introduction to Electric Circuits

3.4 Kirchhoff's voltage law 43

I3R 3 - V + I1R 1

potential differences in that direction are then positive and those in the
opposite direction are negative.
Applying the law to the circuit of Fig. 3.5 we see that for the closed path
containing the nodes 6, 1, 2, 5 and 6, taking the clockwise direction to be
positive,

=0

Figure 3.5

1 13 2 12 3

R3[~ _ R2

6 1- 4

5

rearranging we obtain

V = IIR1 + I3R3 (3.3)

For the closed path containing the nodes 5, 2, 3, 4 and 5, taking the clockwise

direction to be positive,

-I1R1 + V- I2R2 - 0

rearranging we get

V = I1R 1 + 12R2 (3.4)

Finally, for the closed path containing nodes 6, 1, 2, 3, 4, 5 and 6, taking the

clockwise direction to be positive,

I3R 3 - IzR 2 = 0

from which

I2R2 = I3R3 (3.5)

Note that Equation (3.5) is not independent because it could have been

obtained from Equations (3.3) and (3.4) simply by equating their right-hand

sides.

Figure 3.6

A r i

I2

V1 =6V R 2~

E

3fi B 6fi la

[J' I l I ~ c

)V2=4V

D