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Concepts Of Physics MCQ Edition [Volume 2]

Exam: Concepts Of Physics MCQ Edition [Volume 2]
Subject: Physics
Chapter: Electric Current in Conductors

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Electric Current in Conductors

The current flowing through a wire varies with time according to i...

The current flowing through a wire varies with time according to

i = i_0 + \alpha t

, where

i_0 = 10 \text{ A}

and

\alpha = 4 \text{ A s}^{-1}

. Determine the charge that crosses a section of the wire in

10

seconds.

Options

A $100 \text{ C}$
B $200 \text{ C}$
C $500 \text{ C}$
D $300 \text{ C}$

Correct answer

D. $300 \text{ C}$

Step-by-step solution

The current flowing through the wire is given by

i = \dfrac{dq}{dt} = i_0 + \alpha t

The charge

q

crossing a section of the wire in time

t

is obtained by integrating the current:

q = \int_{0}^{t} i \, dt

Substituting the given values

i_0 = 10 \text{ A}

and

\alpha = 4 \text{ A s}^{-1}

:

q = \int_{0}^{10} (10 + 4t) \, dt

q = \left[ 10t + \dfrac{4t^2}{2} \right]_{0}^{10}

q = \left[ 10t + 2t^2 \right]_{0}^{10}

q = 10(10) + 2(10)^2

q = 100 + 200 = 300 \text{ C}

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