Question

An incandescent bulb is designed to operate at $12\text{V}$ DC source. If this bulb is connected to an AC source, and it gives the same brightness, what would be the peak voltage of AC?

• A. $42\sqrt{2}\text{V}$
• B. $32\sqrt{2}\text{V}$
• C. $22\sqrt{2}\text{V}$
• D. $12\sqrt{2}\text{V}$

Answer 1

The correct option is D $12\sqrt{2}\text{V}$

As the brightness is the same, this indicates that heat produced in the two cases is the same.

So, the effective rms current supplied by the AC source is the same as the DC through the bulb.

Thus, effective rms voltage of AC must be $12\text{V}$.

$\therefore E_0=\sqrt{2}{E}_{rms}=12\sqrt{2}\text{V}$