Question

Charge through a cross section of a conductor is given by q=2t square+5t.find the current through the conductor at instant t=2sec

Answer 1

Given:

Charge through a cross section of the conductor is given by ;

$q = 2 {t}^{2} + 5t$

To find:

Current passing through that cross section at t = 2 seconds

Concept:

Current is a scalar quantity represented by the rate of charge flow through the cross section of any conductor.

Calculation:

$q = 2 {t}^{2} + 5t$

$= > i = \dfrac{dq}{dt}$

$= > i = \dfrac{d(2 {t}^{2} + 5t) }{dt}$

$= > i = 4t + 5$

Putting t = 2 second , we get :

$= > i = (4 \times 2) + 5$

$= > i = 13 \: ampere$

So final answer is :

Current at that instant is 13 Amp.

Answer 2

In the above Question , the following information is given -

Charge through a cross section of a conductor is given by -

q = 2t² + 5t

To Find -

We have to find the current flowing through the conductor at the instant, t = 2 seconds .

Solution -

We know that -

$\sf{ I = \dfrac{dQ}{dt} }$

$\sf{ \dfrac{ dQ }{ dt } } \\ \\ \sf{ \implies { \dfrac{ d }{dt } ( 2 t ^ 2 + 5 t ) }} \\ \\ \sf{ \implies { \dfrac{ d }{ dt } 2t ^ 2 + \dfrac{ d }{ dt } 5t }} \\ \\ \sf{ \implies { 4t + 5 }}$

Thus , from the calculations , we obtained the following result -

I = 4t + 5 .

Now , we are asked to find the current flowing through the given conductor at the time instant , t = 2 seconds .

Substituting this value into the equation obtained -

I = 4t + 5

=> I = 4 × 2 + 5

=> I = 13 Amperes .

This is the required answer .

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