Question

Two heater wires of equal length are first connected in series and then in parallel. The ratio of heat produced in the two cases will be

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

Answer 1

The correct option is D $1:4$

Let, R be the resistance of the heater wire. Since, two heater wires are of equal length their resistance is also same.
Hence, for series combination of resistances,
$R_s=2R$
And for parallel combination of resistances,
$R_p=\frac{R}{2}$
Now, heat produced when they first connected in series is
$H_s=\frac{V^2}{R_s}$
where, V is voltage supplied to the heater.
$H_s=\frac{V^2}{2R}$.....................................(1)
heat produced when they first connected in series is
$H_p=\frac{V^2}{R_p}$

$H_p=\frac{V^2}{\frac{R}{2}}$

$H_p=\frac{2V^2}{R}$............................................(2)

From (1) and (2), we get

$\frac{H_s}{H_p}=\frac{\frac{V^2}{2R}}{\frac{2V^2}{R}}\Rightarrow \frac{H_s}{H_p}=\frac{1}{4}$