An e.m.f. of 15 V is applied in a circuit containing a 5 H inductance and a 10 Ω resistance. The ratio of the currents at time t=∞ and, at t=1 second is
Current in the growing circuit is given by
I=I0 ⎡⎢
⎢⎣1−e⎛⎝−RtL⎞⎠⎤⎥
⎥⎦
When, t=∞, I=I0
It=∞=ER=1510=1.5 A
At t=1 sec
It=1=I0⎡⎢
⎢⎣1−e⎛⎝−RL⎞⎠⎤⎥
⎥⎦
=1.5×⎡⎢
⎢⎣1− e⎛⎝−105⎞⎠⎤⎥
⎥⎦
∴It=1=1.5(1−1e2)=1.5(e2−1e2)
Now, It=∞It=1=e2e2−1
Hence, (B) is the correct option.