Question

Four wires of the same diameter are connected in turn between two points, maintained at a constant potential difference. Their resistivities are; $\rho$ and L (wire $1$), $1.2\rho$ and $1.2L$ (wire $2$), $0.9\rho$ and $0.9L$ (wire $3$) and $\rho$ and $1.5L$ (wire $4$). Rank the wires according to the rates at which energy is dissipated as heat, greatest first:

• A. $4>3>1>2$
• B. $4>2>1>3$
• C. $1>2>3>4$
• D. $3>1>2>4$

Answer 1

The correct option is D $3>1>2>4$

$R_1=\frac{\rho L}{A}$,
$R_2=\frac{\left(1.2\rho \right)\left(1.2L\right)}{A}=\frac{1.44\rho L}{A}$,
$R_3=\frac{\left(0.9\rho \right)\left(0.9L\right)}{A}=\frac{0.81\rho L}{A}$,
$R_4=\frac{\rho \left(1.5L\right)}{A}=\frac{1.5\rho L}{A}$
$\therefore R_3<R_1<R_2<R_4$
For constant potential, $H\propto \frac{1}{R}$,
$\therefore H_3>H_1>H_2>H_4$