A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A . If the rate of change of potential difference between the plates is 7 × 10⁸ V / s then the integer value of the distance between the parallel plates is
( Take, ε₀=9 × 10⁻¹² F/m, π=22/7) ____________ μ m.

Solution

Physics sir · 4 steps

Charging current is just C dV/dt, so put C = (ε₀ A)/d in and solve for d.

1. Current and voltage. Charge on a capacitor is q = CV, and C stays fixed while it charges. Differentiating gives i = C dV/dt.

   i = (ε₀ A)/d dV/dt ⇒ d = (ε₀ A)/i dV/dt

2. Plate area. With r = 10 cm = 0.1 m, the area is A = π r² = 22/7 × 0.01 = 0.22/7 m².
3. Put in numbers. d = (9 × 10⁻¹² × 0.22/7 × 7 × 10⁸)/0.15. The 7s cancel, so the top is 1.98 × 10⁻⁴, and dividing by 0.15 gives d = 1.32 × 10⁻³ m.
4. So. 1.32 × 10⁻³ m = 1320 μm, so the answer is 1320.

The common slip: 1.32. Converting 1.32 × 10⁻³ m to millimetres instead of micrometres gives 1.32, not 1320. One micrometre is 10⁻⁶ m.

The idea to keep. For a capacitor being charged, the current is C dV/dt. Combine it with C = (ε₀ A)/d and you can find any one quantity from the others.

Answer from the NTA final answer key. Solution by PrepWiser.