Question

A capacitor is connected to an ac generator that has a frequency of 3.4 kHz and produces a voltage of 2.0 V. The current in the capacitor is 35 mA. When the same capacitor is connected to a second ac generator that has a frequency of 5.0 kHz, the current in the capacitor is 85 mA. What voltage does the second generator produce?

Answer 1

`V_G=3.302857143V`

Step-by-step explanation:

Let´s find the capacitor impedance:

`V=IZ_C`

Using the data provided:

`Z_C=(V)/(I)=(2)/(0.035)=57.14285714` Ω

Now let´s find the capacitance:

`Z_C=(1)/(j2\pi fC )`

`C=(1)/(j2\pi fZ_C) =(1)/(j2\pi (3400)(57.14285714))= 0.8191798542` μF

We can calculate the capacitor impedance for the second case:

`Z_C=(1)/(j2\pi fC)=(1)/(j2\pi (5000)(0.8191798542X10^(-6)) )=38.85714285` Ω

Finally we can calculate the voltage of the second generator:

`V_G=IZ_C=(0.085)(38.85714285)=3.302857143V`