Question

Kitchen Capacitance. The wiring for a refrigerator contains a starter capacitor. A voltage of amplitude 170 V and frequency 60.0 Hz applied across the capacitor is to produce a current amplitude of 0.850 A through the capacitor. What capacitance C is required?

Short answer

The required capacitance,$C=13.3\mu F$

Step-by-step solution

Given Data

A capacitor is a device consisting of two conductors in close proximity that are used to store electrical energy. These conductors are insulated from each other. When a capacitor is attached to an AC supply, the resistance produced by it is called capacitive reactance $\left(X_C\right)$.

The amplitude of voltage, V=170 V

The amplitude of current, l=0.850 A

Frequency of the source, f =60 Hz

Determination of Capacitance required

Capacitive Reactance for an AC source,

$X_C=\frac{V}{I}$

Capacitive reactance in terms of frequency and capacitance is given by,

$X_C=\frac{1}{2\mathrm{\pi fc}}$

By both equation we get,

$$\begin{gathered} \frac{V}{I}=\frac{1}{2\mathrm{\pi fc}} \\ C=\frac{1}{2\mathrm{\pi }fV} \\ C=\frac{0.85}{2\mathrm{\pi }\left(60\right)\left(170\right)} \\ C=13.3*{10}^{-6}F \end{gathered}$$

Therefore, the required capacitance,$C=13.3\mu F$