The current in a conductor varies with time t | vedclass

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(B) The relationship between current $I$ and charge $Q$ is given by $I = \frac{dQ}{dt}$,which implies $dQ = I \, dt$.To find the total charge $Q$ flow

Vedclass · Accepted Answer

$24$

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(B) The relationship between current $I$ and charge $Q$ is given by $I = \frac{dQ}{dt}$,which implies $dQ = I \, dt$.To find the total charge $Q$ flowing between $t = 2 \, s$ and $t = 3 \, s$,we integrate the current with respect to time:$Q = \int_{2}^{3} I \, dt = \int_{2}^{3} (2t + 3t^2) \, dt$$Q = \left[ \frac{2t^2}{2} + \frac{3t^3}{3} \right]_{2}^{3} = \left[ t^2 + t^3 \right]_{2}^{3}$$Q = (3^2 + 3^3) - (2^2 + 2^3)$$Q = (9 + 27) - (4 + 8)$$Q = 36 - 12 = 24 \, C$.

The current in a conductor varies with time $t$ as $I = 2t + 3t^2$,where $I$ is in ampere and $t$ is in seconds. The electric charge flowing through a section of the conductor during $t = 2 \, s$ to $t = 3 \, s$ is ............. $C$.

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