Question

please solve this ..
The cument i through a given cross-section varies with time tasi = 3 + 2t, where i is in ampere and t
is in second. The charge passed through this cross-section during t=0 to t=2s is--
(1) 7C (2) 10C (3)14 C. (4) 20 C​

Answer 1

$\huge\fcolorbox{red}{pink}{Answer \: :}$

✒ Given:

✏ The current I through a cross-section varies with time t as I = 3 + 2t

✒ To Find:

✏ The charge passed through cross-section during t=0 to t=2s

✒Formula:

✏ Formula of current in terms of charge is given by...

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \dag \: \underline{ \boxed{ \bold{ \rm{ \pink{I = \frac{dq}{dt}}}}}} \: \dag$

✒ Calculation:

$\implies \rm \: dq = I \times dt \\ \\ \implies \rm \: q = \displaystyle\int \limits_{0}^{q}dq = \displaystyle \int \limits_{0}^{2}3 + 2t \\ \\ \implies \rm \: q = (3t + {t}^{2} ) \limits_{0}^{2}\\ \\ \implies \rm \: q = 6 + 4 \\ \\ \therefore \: \underline{ \boxed{ \bold{ \rm{ \orange{charge \: flow = 10 \: C}}}}}$

Answer 2

$\huge \underline {\underline{ \mathfrak{ \green{Ans}wer \colon}}}$

Given :

• Time = 3 + 2t

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To Find :

• Charge passed through this cross section during t = 0 to t = 2

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Solution :

As we know that :

$\large{\boxed{\sf{I \: = \: \dfrac{dq}{dt}}}} \\ \\ \rightarrow {\sf{dq \: = \: I dt}} \\ \\ \displaystyle \rightarrow {\sf{ \int \: dq \: = \: \int \: (3 \: + \: 2t) dt}} \\ \\ \displaystyle \rightarrow {\sf{q \: = \: \int _0 ^2 3t \: + \: 2t^2}} \\ \\ \rightarrow {\sf{q \: = \: 3t \: + \: t^2}} \\ \\ \rightarrow {\sf{q \: = \: \big[ 3(2) \: + \: (2)^2\big]}} \\ \\ \rightarrow {\sf{q \: = \: 6 \: + \: 4}} \\ \\ \rightarrow {\sf{q \: = \: 10 \: C}}$