Question

A 10 ohm resistor, 15 mH inductor, and a battery of emf 50.0 V are connected in series through a switch; S. (a) When is the current in the circuit zero? (b) When is the current in the circuit maximum? For both (a) & (b), is it immediately after the switch is closed or long time after the switch is closed? (c) What is the maximum current? (d) What is the time constant of the circuit?

Answer 1

For Growth of current:

(a) At time t = 0, the current in the circuit is zero. Because of self induced emf current will not immediately reach its steady value but grows at a rate depending on inductance and resistance of the c circuit. Hence, immediately the switch is closed.

(b) At t=0 when circuit is first closed current begins to grow at a rate,

        

from the above relation we conclude that greater would be the inductance of the inductor, more slowly the current starts to increase.

Hence, after a long time when the switch is closed.

(c) When the current reaches its steady state value I ,the rate of increase of current becomes zero then from equation (7) we have,
0=(V-IR)/L

Therefore, the maximum current in the circuit is
I=V/R = 50 V/10 ohm = 5 A

(d) The time constant of the circuit is,