Question

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

Answer 1

In the above question given with the data capacitor, voltage and frequency such that initially we use the formula of capacitive reactance. Then by using the RMS value of Current we can solve this question.

Complete step by step answer:
Given:
The capacitance of the capacitor is C=60μF.
The RMS value V=110V.
The frequency of the AC is f=60Hz.
To calculate The RMS value of the current let us use the formula of impedance of the capacitor.We know that the impedance of the capacitor is calculated by:
${X_c} = \dfrac{1}{{\omega C}} \\\ \Rightarrow{X_c} = \dfrac{1}{{2\pi fC}} \\\ \Rightarrow{X_c} = \dfrac{1}{{2 \times 3.14 \times 60 \times 60 \times {{10}^{ - 6}}}} \\\ \Rightarrow{X_c} = 44.2\Omega \\\$
The RMS value of the current is determined as
${I_{rms}} = \dfrac{E}{{{X_c}}} \\\ \Rightarrow{I_{rms}} = \dfrac{{110}}{{44.2}} \\\ \therefore{I_{rms}} = 2.49A \\\$

Hence we find the RMS value of current as $2.49A$.

Note: Capacitive reactance is inversely proportional to the frequency of the alternating voltage therefore for low frequency the capacitive reactance is extremely high and for high frequencies, the capacitive reactance is very low.