Question

A $220V,50HzAC$ source is connected to a $25V,5W$ lamp and an additional resistance $R$ in series (as shown in figure) to run the lamp at its peak brightness, then the value of $R$ (in ohm) will be _____.

Answer 1

Resistance of lamp is:
$R_b=\frac{(25{)}^2}{5}=125\Omega$

RMS current :
$I_{\text{rms}}=\sqrt{\frac{5}{125}}=\frac{1}{5}A$

Solving for $R$:
$\Rightarrow \frac{220}{R+125}=\frac{1}{5}$
$\Rightarrow R=1100-125$
$=975\Omega$