Question

Two wires have resistances $R$ and $2\,R$ . When both are joining in series and in parallel, then ratio of heats generated in these situations on applying the same voltage, is:

• A. 2 : 1
• B. 1 : 2
• C. 2 : 9
• D. 9 : 2

Answer 1

Answer: (C)

In series combination, the net resistance
$R_{s}=R+2 R=3 R$
Heat produced in $R_{s}$,
$H_{s}=\frac{V^{2}}{R_{s}}=\frac{V^{2}}{3 R} \,\,\,...(i)$
In parallel combination, the net resistance
$R_{p}=\frac{R \times 2 R}{R+2 R}=\frac{2 R^{2}}{3 R}=\frac{2}{3} R$
Heat produced in $R_{p}$
$H_{p}=\frac{V^{2}}{R_{p}}=\frac{V^{R}}{2 R / 3}=\frac{3 V^{2}}{2 R} \,\,\,... (ii)$
Dividing Eq. (i) by Eq. (ii), we obtain
$\frac{H_{s}}{H_{p}}=\frac{V^{2} / 3 R}{3 V^{2} / 2 R}=\frac{2}{9}$