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

Answer:

$V_G=3.302857143V$

Explanation:

Let´s find the capacitor impedance:

$V=IZ_C$

Using the data provided:

$Z_C=\frac{V}{I}=\frac{2}{0.035}=57.14285714$ Ω

Now let´s find the capacitance:

$Z_C=\frac{1}{j2\pi fC }$

$C=\frac{1}{j2\pi fZ_C} =\frac{1}{j2\pi (3400)(57.14285714)}= 0.8191798542$ μF

We can calculate the capacitor impedance for the second case:

$Z_C=\frac{1}{j2\pi fC}=\frac{1}{j2\pi (5000)(0.8191798542X10^{-6}) }=38.85714285$ Ω

Finally we can calculate the voltage of the second generator:

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