Question

There are a $25W-220V$ bulb and a $100W-220V$ line. Which electric bulb will glow more brightly?

• A. 25W bulb
• B. 100W bulb
• C. Both will have equal incadescene
• D. Neither 25 W nor 100 W bulb will give light

Answer 1

Answer: (A)

Since power $P$ is given by $P=V^2/R$, so
$R=V^2/P$
For the first bulb,
$R_1=\left(\frac{V^2}{P_1}\right)=\left[\frac{(220{)}^2}{25}\right]=1936\Omega$
For the second bulb,
$R_2=\left(\frac{V^2}{P_2}\right)=\left[\frac{(220{)}^2}{100}\right]=484\Omega$
Current in series combination is the same in the two bulbs and current $i$ is given by
$i=\frac{V}{R_1+R_2}=\frac{220}{1936+484}$
$=\frac{220}{2420}=\frac{1}{11}A$
If the actual powers in the two bulbs be $P_1$ and $P_2$ then
$P_1^{\prime }=i^2{R}_1={\left(\frac{1}{11}\right)}^2\times 1936=16W$
and $P_2^{\prime }=i^2{R}_2={\left(\frac{1}{11}\right)}^2\times 484=4W$
Since $P_1^{\prime }>P_2^{\prime },25W$ bulb will glow more brightly.