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

JEE Main · 2026 · 05 Apr 2026 · Shift 1 · EM Waves

A displacement current of 4.0 A can be set up in the space between two parallel plates of

6 μ F

capacitor. The rate of change of potential difference across the plates of the capacitor is nearly

α \times 1 0^{6}

V/s. The value of

α

is ______.

(A)0.58
(B)0.67✓ Correct
(C)0.82
(D)0.75

Answer: (B)

Solution

The displacement current between the plates equals the current charging the capacitor,

I_{d} = C \frac{d V}{d t}

. With

I_{d} = 4.0

A and

C = 6 \times 1 0^{- 6}

\frac{d V}{d t} = \frac{I _{d}}{C} = \frac{4.0}{6 \times 1 0 ^{- 6}} = 0.667 \times 1 0^{6} V/s

. The rate of change of potential difference is about

0.67 \times 1 0^{6}

V/s, so

α = 0.67

JEE Main · 2026 · 05 Apr 2026 · Shift 1 · Single correct option

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