A 60 μF capacitor is connected to a 110 V, 60 Hz ac supply.

Question:

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

Solution:

Capacitance of capacitor, C = 60 μF = 60 × 10−6 F

Supply voltage, = 110 V

Frequency, ν = 60 Hz

Angular frequency, $\omega=2 \pi v$

Capacitive reactance $X_{\mathrm{c}}=\frac{1}{\omega C}$

$=\frac{1}{2 \pi v C}$

$=\frac{1}{2 \times 3.14 \times 60 \times 60 \times 10^{-6}} \Omega^{-1}$

Rms value of current is given as:

$I=\frac{v}{X_{\mathrm{c}}}$

$=110 \times 2 \times 3.14 \times 60 \times 10^{-6} \times 60=2.49 \mathrm{~A}$

Hence, the rms value of current is 2.49 A.

 

 

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