(B) The charge $q$ passing through a cross-section is given by the integral of current $I$ with respect to time $t$: $q = \int_{t_1}^{t_2} I \, dt$ Gi

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(B) The charge $q$ passing through a cross-section is given by the integral of current $I$ with respect to time $t$: $q = \int_{t_1}^{t_2} I \, dt$ Given $I = 4 + 2t$,$t_1 = 2 \, s$,and $t_2 = 6 \, s$: $q = \int_{2}^{6} (4 + 2t) \, dt$ $q = [4t + t^2]_{2}^{6}$ $q = (4(6) + (6)^2) - (4(2) + (2)^2)$ $q = (24 + 36) - (8 + 4)$ $q = 60 - 12 = 48 \, C$ Thus,the total charge passed is $48 \, C$.

Class 12 Physics Current Electricity Electric Current

Medium

The current in a wire varies with time according to the relation $I = 4 + 2t$. The quantity of charge which has passed through a cross-section of the wire during the time $t = 2 \, s$ to $t = 6 \, s$ will be .............. $C$.

A
$24$
B
$48$
C
$36$
D
$60$

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The current in a wire varies with time according to the relation $I = 4 + 2t$. The quantity of charge which has passed through a cross-section of the wire during the time $t = 2 \, s$ to $t = 6 \, s$ will be .............. $C$.

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$A$ current through a wire depends on time as $i = \alpha_{0} t + \beta t^{2}$ where $\alpha_{0} = 20 \, A/s$ and $\beta = 8 \, As^{-2}$. Find the charge crossed through a section of the wire in $15 \, s$ (in $C$).

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