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Question

A current flowing through a wire depends on time asI=3t2+2t+5. The charge flowing through the cross-section of the wire in time from t=0 to t=2s is:


A

22C

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B

20C

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C

18C

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D

5C

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Solution

The correct option is A

22C


Step 1: Given data

Current-time variation, I=3t2+2t+5

Initial time, t=0

Final time, t=2s

Step 2: Formula used

I=dQdt …………………….(a)

Where (dQ) is the small charge flowing in a small time duration (dt)

Step 3: Calculation of charge flowing through the wire

Substituting the given values in equation (a), we get

3t2+2t+5=dQdt

dQ=(3t2+2t+5)dt …………………(b)

The total charge flowing through the wire can be calculated by integrating the equation (b) over limits t=0 to t=2s

Integration equation (b), we get

dQ=02(3t2+2t+5)dtQ=023t33+2t22+5tQ=t302+t202+5t02Q=(2)3+(2)2+5(2)Q=8+4+10Q=22C

Hence, option (a) is correct.


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