Question

A circuit element is placed in a closed box. At time t=0, constant current generator supplying a current of 1 amp, is connected across the box. Potential difference across the box varies according to graph shown in figure. The element in the box is :

• A. resistance of $2\Omega$
• B. battery of emf 6 V
• C. inductance of 2 H
• D. capacitance of 0.5F

Answer 1

The correct option is D capacitance of 0.5F

Voltage across a resistance is given by $V=IR$, thus, does not vary with time.

Voltage across inductance is given by $V=L\frac{di}{dt}$, since $i$ is constant, voltage across inductance should remain $0$.

Voltage across capacitance is given by $V=\frac{1}{C}\int idt$, since i is constant $V\propto t$ & given by $V=\frac{t}{C}$.

Here slope of the graph is 2. If we choose $C=0.5,\frac{1}{C}=2$.

Thus. the element in the box can be capacitance of $0.5F$.