(A) The relationship between current $I$ and charge $q$ is given by $I = \frac{dq}{dt}$.Therefore,the charge $dq$ is $dq = I \, dt = (3t^2 + 2t + 5) \

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(A) The relationship between current $I$ and charge $q$ is given by $I = \frac{dq}{dt}$.Therefore,the charge $dq$ is $dq = I \, dt = (3t^2 + 2t + 5) \, dt$.To find the total charge $q$ passing through the cross-section from $t = 0$ to $t = 2$ seconds,we integrate the expression:$q = \int_{0}^{2} (3t^2 + 2t + 5) \, dt$$q = [t^3 + t^2 + 5t]_{0}^{2}$Substituting the limits:$q = (2^3 + 2^2 + 5(2)) - (0^3 + 0^2 + 5(0))$$q = (8 + 4 + 10) - 0 = 22 \, C$.Thus,the total charge is $22 \, C$.

Class 12 Physics Current Electricity Electric Current

Medium

The current flowing through a wire varies with time according to the formula $I = 3t^2 + 2t + 5$. The total charge passing through a cross-section of the wire in the interval from $t = 0$ to $t = 2$ seconds is ........... $C$.

A
$22$
B
$20$
C
$18$
D
$5$

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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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The current flowing through a wire varies with time according to the formula $I = 3t^2 + 2t + 5$. The total charge passing through a cross-section of the wire in the interval from $t = 0$ to $t = 2$ seconds is ........... $C$.

Similar Questions

$A$ $60\,W$ bulb carries a current of $0.5\,A$. The total charge passing through it in $1$ hour is ............ $C$.

$A$ current of $5\,A$ flows through a resistance of $10\, \Omega$ for $4$ minutes. The total charge in Coulombs and the number of electrons passing through any cross-section of the resistor in this time are, respectively:

If an electron revolves in a circular path of radius $0.5 \times 10^{-10} \ m$ at a frequency of $5 \times 10^{15} \ Hz$,the electric current in the circle is .................. $mA$. (Charge of an electron $= 1.6 \times 10^{-19} \ C$)

The quantity $X = \frac{\varepsilon_0 LV}{t}$,where $\varepsilon_0$ is the permittivity of free space,$L$ is length,$V$ is potential difference,and $t$ is time. The dimensions of $X$ are the same as those of:

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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