Question

Two identical heater wires are first connected in series and then in parallel with a source of electricity.

The ratio of heat produced in the first case to heat produced in second case is:

• A. $4:1$
• B. $1:2$
• C. $2:1$
• D. $1:4$

Answer 1

The correct option is D $1:4$

Since, both heater wires are identical. So, resistance of each wire is $R$. When they are connected in series, then total resistance :

$R_s=R+R=2R$
Heat produced, $H_1=\frac{V^{2}t}{2R}\to$ ....ii
When they are connected in parallel then
$R_p=\frac{R}{2}$
Heat produced $H_2=\frac{2V^{2}t}{R}$ ...(ii)
From (i) and (ii)
$\frac{H_1}{H_2}=\frac{1}{4}$