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Question

The time constant of an LR circuit is 20 ms The circuit is connected at t = 0 and the steady-state current is found to be 4A. Find the current at 80 ms.


A

0.98 A

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B

1 A

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C

0.44 A

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D

0.88 A

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Solution

The correct option is D

0.88 A


Explanation for the correct answer:-

Step 1: Given Data

Time constant, τ=20ms

i0=4A

t=80ms

Step 2: Formula used,

i=i0(1et/τ)

i is the circuit current.

i0 is the steady state value of the current.

τ is the time constant.

t is the time taken

Step 3: Calculating the current at 80 ms

i=i0(1et/τ) Given, i0=4A at t=0, t=80ms=80×10-3s, τ=20ms=20×10-3s

i=4(1e-τt)

i=4(1e20×10-3/80×10-3)

i=4(1e(1/4))i=4(1e(0.25))i=4(10.778)i=0.88A

Hence, option D is the correct answer.


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