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A solenoid of inductance 50 mH and resi...

A solenoid of inductance 50 mH and resistance `10 Omega` is connected to a battery of 6V. Find the time elapsed before the current acquires half of its steady - state value.

A

`3.5 ms`

B

`2.5 ms`

C

`0.693 ms`

D

`2 ms`

Text Solution

Verified by Experts

The correct Answer is:
A
Time constant of circuit= `L/R =(50 mH)/(10)=5 ms`
Current at time T is given by
`i=i_(0)(1-e^(-T//(tau)))`
`e^(-T//(tau)) = 1/2 or T/(tau)=log_(e)2`
`T=tau log_(2)2 = 5 ms xx 0.693 = 3.2 ms`.
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