Question

An electric bulb is designed to operate at $220\text{V}DC$. If this bulb is connected to an $AC$ source, it gives the same brightness. What would be the peak voltage of $AC$?

• A. $220\text{V}$
• B. $220\sqrt{2}\text{V}$
• C. $\frac{220}{\sqrt{2}}\text{V}$
• D. $\sqrt{220}\text{V}$

Answer 1

The correct option is B $220\sqrt{2}\text{V}$

As brightness is same in both the cases, this indicates that heat produced in the two cases is the same, so the effective $rms$ current supplied by $AC$ source is the same as that of $DC$ current through the bulb.

Thus, effective $rms$ voltage of $AC$ must be $220\text{V}$, which is given in terms of peak value of voltage as

$E_{rms}=\frac{E_o}{\sqrt{2}}$

$\Rightarrow E_0=\sqrt{2}{E}_{rms}=220\sqrt{2}\text{V}$

Hence, $\left(B\right)$ is the correct option.