Ncert Exercises & Solutions

Question 7.4 :

A 60 µF capacitor is connected to a 110 V, 60 Hz ac supply. Determine the rms value of the current in the circuit.

Given:

The capacitance of the capacitor in the circuit is C = 60 μF or 60 × 10 ^{– 6} F

The source voltage is V = 110 V

The frequency of the source is ν = 60 Hz

The angular frequency can be calculated using the following relation,

ω = 2πν

Capacitive reactance,

$XC = 1 {ωCX}_{C} = \frac{1}{ωC} = \frac{1}{2 πνC} = \frac{1}{2 π \times 60 \times 60 \times 10^{- 6}} Ω$

the rms value of the current is given as:

$I = \frac{V}{X_{C}} = \frac{220}{2 π \times 60 \times 60 \times 10^{8}} = 2.49 A$

Hence, the rms value of the current is 2.49 A.