Question

The peak voltage of an AC supply 440V, then its rms voltage is:
(A) 31.11V
(B) 311.1V
(C) 41.1V
(D) 411.1V

Answer 1

Hint: In this problem, we will first relate the maximum voltage in an AC supply with its rms (root mean square) voltage. The root mean square voltage in an AC circuit is equal to maximum voltage of the AC supply divided by root two. We shall use this to proceed in our problem and also see the conditions at which we can get a maximum voltage supply in an AC circuit.

Complete answer:
Let us first assign some terms that we are going to use in our problem.
Let the peak voltage supply in the circuit be equal to ${{V}_{\max }}$ volts. Then, its value has been given in the problem as:
$\Rightarrow {{V}_{\max }}=440V$ [Let this expression be termed as equation number (1)]
Now, let the rms or root mean square voltage, in the circuit be given by ${{V}_{rms}}$ . Then, this root mean square voltage can be calculated using the following formula:
$\Rightarrow {{V}_{rms}}=\dfrac{{{V}_{\max }}}{\sqrt{2}}$ [Let this expression be termed as equation number (2)]
Now, using the value of peak voltage from equation number (1) and using it in equation number (2), we can calculate the root mean square voltage as:
$\Rightarrow {{V}_{rms}}=\dfrac{440}{\sqrt{2}}$
Now using, $\sqrt{2}=1.414$, in the above expression. The expression simplifies into:
$\begin{align}
 & \Rightarrow {{V}_{rms}}=\dfrac{440}{1.414}V \\
 & \therefore {{V}_{rms}}=311.1V \\
\end{align}$
Hence, the root mean square voltage for a peak voltage supply of 440V in an AC supply comes out to be 311.1V .

So, the correct answer is “Option B”.

Note: As the name suggests, peak voltage. It is the highest voltage that can be generated by an AC supply. On dividing this peak voltage by the total impedance of the circuit, we get the peak current in the circuit. And the rms current in the circuit is obtained by dividing this peak current by a factor of root two. These are some of the most basic relations and should be remembered always.