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Standard X

Physics

Electric Current and Potential

The current i...

Question

The current in a conductor varies with time t as $I = 3 t + 4 t^{2}$ , where I is in amperes and t in seconds. The electric charge that flows through the section of the conductor between t = 1 s and t = 3 s is

$\frac{14}{3} C$

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$\frac{3}{14} C$

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$\frac{140}{3} C$

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$\frac{3}{140} C$

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Solution

The correct option is C
$\frac{140}{3} C$

Charge, $Q = \int I d t = \int_{1}^{3} (3 t + 4 t^{2}) d t = {[\frac{3 t^{2}}{2} + \frac{4 t^{3}}{3}]}_{1}^{3} = \frac{27}{2} + \frac{108}{3} - \frac{3}{2} - \frac{4}{3} = \frac{140}{3} C$

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The current in a conductor varies with time t as I=3t+4t2, where I is in amperes and t in seconds. The electric charge that flows through the section of the conductor between t = 1 s and t = 3 s is

The correct option is C 1403 C Charge, Q=∫Idt=∫31(3t+4t2)dt=[3t22+4t33]31=272+1083−32−43=1403 C

The current in a conductor varies with time t as $I = 3 t + 4 t^{2}$ , where I is in amperes and t in seconds. The electric charge that flows through the section of the conductor between t = 1 s and t = 3 s is

The correct option is C
$\frac{140}{3} C$

Charge, $Q = \int I d t = \int_{1}^{3} (3 t + 4 t^{2}) d t = {[\frac{3 t^{2}}{2} + \frac{4 t^{3}}{3}]}_{1}^{3} = \frac{27}{2} + \frac{108}{3} - \frac{3}{2} - \frac{4}{3} = \frac{140}{3} C$