A capacitor is connected to an ac generator that has a frequency of 2.3 kHz and produces a rms voltage of 1.5 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 85 mA. What rms voltage does the second generator produce

Given that,

AC frequency of 2.3KHz

f=2.3*10³Hz

Vrms produce is

Vrms=1.5V

Current rms

Irms = 31mA

The capacitor is reconnected to a generator of frequency

f=4.8KHz = 4800Hz

The current rms becomes

Irms = 85mA

Vrms=?

Solution

First genrator

The capacitive reactance is given as

Xc=Vrms/Irms

Xc=1.5/31*10^-3

Xc=48.39 ohms

Now, to know the capacitance of the capacitor

Xc=1/2πfC

Then,

C=1/2πfXc

So,

C=1/2*π*2300*48.39

C=1.43*10^-6C

C=1.43μF

Note: the capacitance of the capacitor did not change,

Now for generator two.

The reactance are given as

Xc=1/2πfC

Xc=1/2*π*4800*1.43*10^-6

Xc=23.19ohms

Then,

Vrms2=Irms2 * Xc

Vrms2=85*10^-3*23.19ohms

Vrms2=1.97V

Vrms2=1.97Volts