Question

A bulb draws $24\text{W},$ when connected to a $12\text{V}$ supply. Find the power if it is connected to a $6\text{V}$ supply.
(Neglect resistance change due to unequal heating in the two cases.)

• A. $2\text{W}$
• B. $4\text{W}$
• C. $6\text{W}$
• D. $8\text{W}$

Answer 1

The correct option is C $6\text{W}$

We have
$P=\frac{v^2}{R}$
$24\text{W}=\frac{(12V{)}^2}{R}$ ...(i)
Suppose the bulb draws power $P_1,$ when connected to the $6\text{V}$ battery. Then,

$P_1=\frac{(6V{)}^2}{R}$ ...(ii)
From (i) and (ii), we have
$\frac{P_1}{24}=\frac{(6V{)}^2}{(12V{)}^2}=\frac{1}{4}$

$P_1=\frac{24}{4}=6\text{W}$