Question

The voltage across the terminals of an ac power supply varies with time according to Eq. (31.1). The voltage amplitude is V=45.0 V. What are (a) the root mean-square potential difference${\mathbf{V}}_{\mathbf{rms}}$and (b) the average potential difference${\mathbf{V}}_{\mathbf{avg}}$between the two terminals of the power supply?

Short answer

The root mean square potential difference ${\mathrm{V}}_{\mathrm{rms}}$=31.8V and ${\mathrm{V}}_{\mathrm{avg}}$=0

Step-by-step solution

Step-1: Formulas used  

The maximum value of the voltage${\mathbf{V}}_{\mathbf{max}}$is the amplitude of the voltage wave

${\mathbf{V}}_{\mathbf{rms}}\mathbf{=}\frac{{\mathbf{V}}_{\mathbf{max}}}{\sqrt{\mathbf{2}}}$, where is ${\mathbf{V}}_{\mathbf{r}\mathbf{m}\mathbf{s}}$the root mean square voltage.

Step-2: Calculation for root mean square voltage Vrms  

$$\begin{gathered} {\mathrm{V}}_{\mathrm{rms}}=\frac{45\mathrm{V}}{\sqrt{2}} \\ =31.8\mathrm{V} \end{gathered}$$

Step-3: Calculation for average potential difference Vavg

In opposite to the current, the voltage has no average value. Because it is a sinusoidal wave, and between the two terminals of the power supply, so average potential difference is 0

Therefore the root mean square potential difference ${\mathrm{V}}_{\mathrm{rms}}$=31.8V and ${\mathrm{V}}_{\mathrm{avg}}$=0