Question

The current through a wire depends on time as I = 10 + alpha ×t, where 10 = 10 A and
a = 4 As-1. Find the charge that flows across a section of the wire in 10 seconds.
(Ans. 300 C)​

Answer 1

Current is a function of time as follows :

$I = 10 + \alpha t$

To find:

Charge passing through the cross - section of a conductor in 10 secs.

Concept:

Current is defined as the rate of flow of charge through a cross - section of a wire.

So in an differential manner , we cans say that :

$\boxed{ \displaystyle \int \: dq = \int I \: \times dt \: }$

Calculation:

$\displaystyle \int \: dq = \int I \: \times dt$

$= > \displaystyle \int \: dq = \int (10 + \alpha t)\: \times dt$

$= > \displaystyle \int \: dq = \int 10 \: dt+ \int \alpha t \: dt$

$= > q = 10t + \dfrac{ \alpha {t}^{2} }{2}$

Putting available values and limits :

$= > q = (10 \times 10)+ \dfrac{ 4 \times {(10)}^{2} }{2}$

$= > q = 300 \: coulomb$

So final answer :

Charge Passed = 300 C

Answer 2

Answer:

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