Question

In the circuit diagram ,heat produces in $R,2R$ and $1.5R$ are in the ratio

• A. 4 : 2 : 3
• B. 8 : 4 : 27
• C. 2 : 4 : 3
• D. 27 : 8 : 4

Answer 1

Answer: (B)

We have, $l_1=\frac{l\times 2R}{3R}=\frac{2l}{3}$
$\therefore H_1=l_1^{2}R=\frac{4l^2}{9}\times R...(i)$
Also, $I_2=\frac{l\times R}{3R}=\frac{1}{3}$
$\therefore H_2=l_2^2(2R)=\frac{l^2}{9}\times 2R...(ii)$
and $H_3=R^2(1.5R)...(ii)$
From Eqs. (i), (ii) and (iii),
$H_1:H_2:H_3=\frac{4l^2}{9}\times R:\frac{R^2}{9}\times 2R:R^2\times 1.5R$
$=\frac{4}{9}:\frac{2}{9}:1.5=4:2:13.5$
$=8:4:27$