Question

Two electric bulbs rated $25W,220V$ and $100W,200V$ are connected in series across $a$ $220V$ source. The $25W$ and $100W$ bulbs now draw powers $P_1$ and $P_2$ respectively, then :
(1) $P_1=16W$
(3) $P_2=16W$
(2) $P_1=4W$
(4) $P_2=4W$.

• A. 1 and 2 are correct
• B. 2 and 3 are correct
• C. 1 and 4 are correct
• D. 1, 2 and 3 are correct

Answer 1

Answer: (C)

Resistance of first bulb.
$R_1=\frac{V_1^2}{P_1}=\frac{(220{)}^2}{25}$
Resistance of second bulb
$R_2=\frac{V_2^2}{P_2}=\frac{(220{)}^2}{100}$
Net resistance in series combination will be
$R=R_1+R_2=$
$\frac{(220{)}^2}{25}+\frac{(220{)}^2}{100}=\frac{(220{)}^2\times 5}{100}=\frac{(220{)}^2}{20}$
Current through the circuit,
$I=\frac{V}{R}=\frac{220}{(220{)}^2/20}=\frac{20}{220}=\frac{1}{11}A$
Power in $25W$ bulb,
$P_1=I^2{R}_1$
$={\left(\frac{1}{11}\right)}^2\times \frac{(220{)}^2}{25}=16W$
Power in $100W$ bulb,
$P_2=I^2{R}_2$
$={\left(\frac{1}{11}\right)}^2\times \frac{(220{)}^2}{100}=4W$