The rms value of conduction current in a parallel plate capacitor is 6.9 μ A. The capacity of this capacitor, if it is connected to 230 V ac supply with an angular frequency of 600 rad / s, will be :

Solution

Physics sir · 3 steps

Treat the capacitor like a resistor whose resistance is X_C = 1/(ω C), then use Ohm's law.

1. Capacitive reactance. In an ac circuit a capacitor opposes current through its reactance X_C = 1/(ω C). Ohm's law then links the rms values: Iᵣₘₛ = Vᵣₘₛ/X_C = Vᵣₘₛ ω C.

   C = Iᵣₘₛ/(Vᵣₘₛ ω)

2. Put in numbers. The denominator is 230 × 600 = 1.38 × 10⁵. So C = (6.9 × 10⁻⁶)/(1.38 × 10⁵) = 5 × 10⁻¹¹ F.
3. So. 5 × 10⁻¹¹ F = 50 × 10⁻¹² F = 50 pF, which is option (b).

The idea to keep. For a pure capacitor, Iᵣₘₛ = Vᵣₘₛ ω C. Write every quantity in SI units first, and convert to pF only at the end, since 1 pF = 10⁻¹² F.

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