Electric current through a conductor varies with time as i = at2 where ‘a’ is a constant. Total charge flows through a cross section in time t1=0 to t2=2secis

q=∫i dtq=a∫02t2dtq=at3320q=a×83

Electric current through a conductor varies with time as i = at2 where ‘a’ is a constant. Total charge flows through a cross section in time t1=0 to t2=2secis

q=∫i dtq=a∫02t2dtq=at3320q=a×83

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Electric current through a conductor varies with time as i = at² where ‘a’ is a constant. Total charge flows through a cross section in time $t_{1} = 0$ to $t_{2} = 2 \sec$ is

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$\frac{a \times 8}{7} u n i t$

$a \times 8 u n i t$

$\frac{a \times 8}{3} u n i t$

$\frac{a \times 8}{5} u n i t$

answer is C.

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Detailed Solution

$q = \int i d t$

$q = a \int_{0}^{2} t^{2} d t$

$q = a {[\frac{t^{3}}{3}]}^{2}_{0}$

$q = \frac{a \times 8}{3}$

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Electric current through a conductor varies with time as i = at2 where ‘a’ is a constant. Total charge flows through a cross section in time t1=0 to t2=2secis

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Electric current through a conductor varies with time as i = at² where ‘a’ is a constant. Total charge flows through a cross section in time $t_{1} = 0$ to $t_{2} = 2 \sec$ is