A 10 μF capacitor is connected to a 210 V, 50 Hz source as shown in figure. The peak current in the circuit is nearly ​

Question

A  \(10\ \mu F\) capacitor is connected to a 210 V, 50 Hz source as shown in figure. The peak current in the circuit is nearly (\(\pi\) = 3.14):

(1) 0.58 A 

(2) 0.93 A 

(3) 1.20 A 

(4) 0.35 A

Answer 1

Correct option is : (2) 0.93 A 

Capacitive Reactance \(X_C = \frac{1}{\omega C} = \frac{1}{2 \pi fC}\) 

\(= \frac{1}{2 \times3.14\times50\times10\times10^{-6}}\)

\( = \frac{1000}{3.14}\)

\(V_{rms} = 210 \ V\) 

\(i_{rms} = \frac{V_{rms}}{X_c} = \frac{210}{X_c}\) 

Peak current \(= \sqrt{2i}_{rms} = \sqrt{2}\times\frac{210}{1000}\times3.14 = 0.932\)

\(\simeq0.93 \ A\)