Current passing through a wire as function of time is given as (t) = 0.02 t + 0.01 A. The charge that will flow through the wire from t = 1s to t = 2s is: [2025]

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Solution

Q.
Current passing through a wire as function of time is given as $I$ (t) = 0.02 t + 0.01 A. The charge that will flow through the wire from t = 1s to t = 2s is: [2025]

1 0.06 C

2 0.02 C

3 0.07 C

4 0.04 C

Ans.
(4)

$q = \int i d t = \int_{1}^{2} (0.02 t + 0.01) d t$

$q = {[0.02 \frac{t^{2}}{2} + 0.01 t]}_{1}^{2}$

$= \frac{0.02}{2} \times (2^{2} - 1^{2}) + 0.01 \times 1 = 0.04 C$

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