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Question: Current in a resistor depends on time t is given by i = at where a is a positive constant. The charg...

Current in a resistor depends on time t is given by i = at where a is a positive constant. The charge transferred in time interval 0 to t0 will be –

A

at0

B

at02

C

αt023\frac{\alpha t_{0}^{2}}{3}

D

αt022\frac{\alpha t_{0}^{2}}{2}

Answer

αt022\frac{\alpha t_{0}^{2}}{2}

Explanation

Solution

i = at = dqdt\frac{dq}{dt} Ž ∫dq=∫0t0αtdt\int_{}^{}{dq} = \int_{0}^{t_{0}}{\alpha tdt} Ž q = αt022\frac{\alpha{t_{0}}^{2}}{2}