Question

A coil of inductance 8.4 mH and resistance $6 \Omega$ is connected to a 12 V battery. The current in the coil is 1A at approximately the time

• A. 500 s
• B. 20 s
• C. 35 ms
• D. 1 ms

Answer 1

Answer: (D)

1 ms

Answer 2

The current-time (i-t) equation in L-R circuit is given by
[Growth of current in L-R circuit]
i = $i_0 \, (1 - e^{ - t / \pi L} )$ \hspace20mm ...( i)

where $i_0 = \frac{V}{ R} = \frac{12}{ 6 } = 2 A$
and $T_L = \frac{L}{R} = \frac{ 8.4 \times 10^{ - 3 }}{ 6 }$
= 1.4 $\times 10^{ - 3}$ s
and i = 1 A \hspace20mm (given)
t = ?
Substituting these values in E (i), we get
t = 0.97 $\times 10^{ - 3 }$ s
or t = 0.97 ms
t = 1 ms.