Question

A capacitor is connected to an ac generator that has a frequency of 3.0 kHz and produces a rms voltage of 2.0 V. The rms current in the capacitor is 31 mA. When the same capacitor is connected to a second ac generator that has a frequency of 4.8 kHz, the rms current in the capacitor is 74 mA. What rms voltage does the second generator produce

Answer 1

Answer:

In second case voltage will be 2.986 volt

Explanation:

In first case we have given frequency f = 3 kHz = 3000 Hz

Voltage v = 2 volt

Current i = 1 mA

So capaitive reactance $X_C=\frac{V}{i}=\frac{2}{31\times 10^{-3}}=64.5161ohm$

$X_C=\frac{1}{\omega C}$

So $64.5161=\frac{1}{2\times 3.14\times 3000\times C}$

$C=8.22\times 10^{-7}F$

In second case frequency f =4.8 kHz = 4800 Hz

Capacitive reactance $X_C=\frac{1}{\omega C}=\frac{1}{2\times 3.14\times 4800\times 8.22\times 10^{-7}}=40.3577ohm$

Current i = 74 mA

So voltage $V=iX_C=74\times 10^{-3}\times 40.3577=2.986volt$