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Question

A displacement current of 4.0 A can be set up in the space between two parallel plates of $6\mu\text{ }F$ capacitor. The rate of change of potential difference across the plates of the capacitor is nearly $\alpha \times 10^{6}\text{ }V/s$. The value of $\alpha$ is $\_\_\_\_$ .

Options

A.0.58
B.0.67
C.0.82
D.0.75

Solution

Sol. [Key Concept: Displacement current $I_{d} = C\frac{dV}{dt}$; solve for $\frac{dV}{dt}$.]

$$I_{d} = C\frac{dV}{dt}$$

$$\begin{matrix} & 4 = \left( 6 \times 10^{- 6} \right)\left( \alpha \times 10^{6} \right) \\ & \alpha = \frac{2}{3} \approx 0.67 \end{matrix}$$

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