Chapter 2, Problem 2.1MCQ

The rms value of $v\left(t\right)={\text{V}}_{\max }\cos \left(\omega t+\delta \right)$ is given by

a. ${\text{V}}_{\max }$

b. ${\text{V}}_{\max }/\sqrt{2}$

c. ${\text{2V}}_{\max }$

d. $\sqrt{2}{\text{V}}_{\max }$

To determine

The rms value of the voltage function $v\left(t\right)$.

Answer to Problem 2.1MCQ

The option (b) is correct, therms value of the voltage function $v\left(t\right)$ is $\frac{V_{\max }}{\sqrt{2}}$.

Explanation of Solution

Given:

The expression for voltage $v\left(t\right)$ is.

$v\left(t\right)=V_{\max }\cos \left(\omega t+\delta \right)$

Concept used:

Write the standard sinusoidal expression for voltage $v\left(t\right)$.

$v\left(t\right)=v_{\text{m}}\cos \left(\omega t+\varphi \right)$   ...............(1)

Here, $v_{\text{m}}$ is the maximum value of sinusoidal voltage, $\omega$ is angular frequency, $t$ is the time and $\varphi$ is the phase shift.

Write the expression for rms value of voltage.

$v_{\text{rms}}=\frac{v_{\text{m}}}{\sqrt{2}}$   ...............(2)

Here, $v_{\text{rms}}$ is the rms value of voltage.

Calculation:

Compare equation (1) with given expression.

$v_{\text{m}}=V_{\max }$

Substitute $V_{\max }$ for $v_{\text{m}}$ in equation (2).

$v_{\text{rms}}=\frac{V_{\max }}{\sqrt{2}}$

The rms value of the voltage function $v\left(t\right)$ is $\frac{V_{\max }}{\sqrt{2}}$.

Conclusion:

Thus, option $\left(\text{b}\right)$ is correct, therms value of the voltage function $v\left(t\right)$ is $\frac{V_{\max }}{\sqrt{2}}$.