# A coil of inductance 8.4 mh and resistance 6 Ω is connected to a 12 V battery. The current in the coil is 1.0 A approximately after time Option 1) 500 ms   Option 2) 20 ms Option 3) 35 ms   Option 4)  1 ms

Self Inductance -

An emf is induced in the coil or the circuit which oppose the change that causes it. Which is also known back  emf.

- wherein

$i=i_{0}(1-e^{-t/T})$

$\left [ T=\frac{1}{R}=\frac{8.4mH}{6\Omega }=1.4ms \right ]$

$i_{0}=\frac{e}{R}=\frac{12}{6}=2A$

$i=1A$

$=> 1=2(1-e^{-t/T})$

$=>e^{-t/T}=\frac{1}{2}$

$=> \frac{t}{T}=l_{n}2$

$=>t=(0.693)T$

$=> t=(0.693)T$

$=> t= 1ms$

Option 1)

500 ms

Option is incorrect

Option 2)

20 ms

Option is incorrect

Option 3)

35 ms

Option is incorrect

Option 4)

1 ms

Option is correct

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