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Current passing through a wire as function of time is given as I(t)=0.02t+0.01 A. The charge that will flow through the wire from t=1 s to t=2 s is

Asked in JEE Main 4th April 1st Shift 2025 · Current and charge flow

(1) 0.07 C
(2) 0.04 C
(3) 0.06 C
(4) 0.02 C

Answer: (2) 0.04 C

Step-by-step solution

q=∫₁² I dt=∫₁²(0.02t+0.01) dt

=0.01 (t²)|₁²+0.01 (t)|₁²

=0.01×3+0.01×1

q=0.04 C

Why the other options are wrong

(1) Integrates 0.02t as 0.02t², forgetting the factor 1/2: 0.02(4-1)+0.01=0.07.
(3) Integrates from t=0 to t=2 s instead of from 1 to 2.
(4) Takes the change in current I(2)-I(1)=0.02 as the charge.

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