Question

Two heater wires, made of the same material and having the same length and the same radius, are first connected in series and then in parallel to a constant potential difference. If the rates of heat produced in the two cases are $H_s$ and $H_p$ respectively, then $H_s/H_p$ will be

• A. 1/2
• B. 2
• C. 1/4
• D. 4

Answer 1

Answer: (C)

When heater wires are connected in series, then equivalent resistance,
$R_s=R_1+R_2=2R\left(\because R_1=R_2\right)$
Rate of heat produced, $H_s=\frac{V^2}{R_s}$
$H_s=\frac{V^2}{2R}$...(i)
In second case, $R_p=\frac{R_1+R_2}{R_1+R_2}=\frac{R\times R}{2R}$
or $R_p=\frac{R}{2}$
$\therefore$ Rate of heat produced, $H_p=\frac{V^2}{R_p}$
$H_p=\frac{2V^2}{R}$...(ii)
Dividing (i) by (ii), we get
$\frac{H_s}{H_p}=\frac{\left(V^2/2R\right)}{\left(2V^2/R\right)}$ $=\frac{V^2}{2R}\times \frac{R}{2V^2}=\frac{1}{4}.$