Current Electricity

JEE Main level, single correct, medium

9 of 380

Question 9 of 380

The electric current through a wire varies with time as I=I0+βtI={I}_{0}+\beta t, where I0=20A{I}_{0}=20A and β=3As−1\beta =3A{s}^{-1}. The amount of electric charge crossed through a section of the wire in 20s20s is:

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Answer: (B) 1000C1000C

Given that
Current I=I0+βtI={I}_{0}+\beta t, I0=20A{I}_{0}=20A and β=3As−1\beta =3A{s}^{-1}
The instantaneous current is given by
I=20+3t...(1)I=20+3t...\left(1\right)
Integrating equation (1), we have
dqdt=20+3t⇒∫0qdq=∫020(20+3t)dt⇒q=∫02020dt+∫0203tdt⇒q=[20t+3t22]020=1000C\dfrac{dq}{dt}=20+3t \Rightarrow {\int }_{0}^{q}dq={\int }_{0}^{20}(20+3t)dt \Rightarrow q={\int }_{0}^{20}20dt+{\int }_{0}^{20}3tdt \Rightarrow q={\left[20t+\dfrac{3{t}^{2}}{2}\right]}_{0}^{20} =1000C

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