Chapter 21, Problem 63P

To determine

The frequency of the ac voltage source

Answer to Problem 63P

Solution:

The frequency of the ac voltage source will be $270\text{Hz}$

Explanation of Solution

Given:

$\begin{array}{l}C=1.0\mu F\\ R=650\Omega \\ I_{rms}=4.0V,3.0V,7.7V\end{array}$

Formula Used:

$f=\frac{I_{rms}}{2\pi C{V}_c}$

Where,

$V=$ Voltage

$I=$ Current

$C$= capacitor

Calculation:

$f=\frac{I_{rms}}{2\pi C{V}_c}=\frac{V_R}{2\pi CR{V}_c}$

$\frac{V_R}{2\pi CR{V}_c}=\frac{\left(3.0V\right)}{2\pi \left(1.0\times {10}^{-6}C\right)\left(650\Omega \right)\left(2.7V\right)}=2721.1Hz=270\text{Hz}$

Since the voltage in the resistor and capacitor are not in phase, the $\text{rms}$ voltage across the power source will not be the sum of the $\text{rms}$ voltage across the resistor and capacitor.