Introduction to Electric Circuits

8.2 Circuits containing resistance and inductance 177

Equation (8.9) represents an exponential decay of current, Equation (8.10)

represents an exponential decay of voltage and Equation (8.11) describes an

exponential rise of voltage starting from -V and aiming towards zero. These

are illustrated in Fig. 8.6(a) and (b).

i

I

o rt

(a)

Figure 8.6

-V

S

(b)

t

Example 8.3

A circuit consisting of a resistor having a resistance of 2 1~ in series with an

inductor whose inductance is 10 H is fed from a 12 V d.c. supply. Thirty seconds

after the circuit has been switched on a fault causes the supply to become short

circuited. Determine the current in the circuit 2.5 s after the occurrence of the

fault.

Solution

i 20- 1OH i 2D. 1OH

A >-~'---! i ,,-Y~r-v-~____ A )__~__ I I

v()

B B

Figure 8.7

(a) (b)

Fig. 8.7(a) shows the circuit before the fault occurs and Fig. 8.7(b) shows the

circuit after the fault. The time constant of the circuit is given by

~"- L/R - 10,/2 - 5 s. After 30 s (which is 6 ~-) therefore, the current will have

reached its steady state value:

I- WR -12/2 = 6 A

When the fault occurs I = 6 A and 2.5 s later

i - I exp (-Rt/L) - 6 exp (-2 x 2.5,/10) - 3.64 A