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Q.

A variable current flows through a $1 Ω$ resistor for 2s. time dependence of the Current is shown in the graph

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a

Average current through the resistor is 5 A

b

Total charge flown through the resistor is 10 C

c

Maximum power during the flow of current is 100 W

d

Total heat produced in the resistor is 50 J

answer is A, B, D.

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Detailed Solution

$\begin{array}{l} T o t a l c h \arg e = \int I d t = A r e a u n d e r t h e c u r v e = 10 C \\ A v e r a g e c u r r e n t = \frac{\int I d t}{\int d t} = 5 A \\ T o t a l h e a t p r o d u c e d = \int I^{2} d t \\ = \int_{0}^{2} {(- 5 t + 10)}^{2} 1 d t = \frac{200}{3} J \end{array}$

Maximum power= $= I^{2} R w h e n I i s \max i m u m c u r r e n t = 100 \times 1 = 100 W$

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