Question

Heater of an electric kettle is made of a wire of length L and diameter d. It takes 4 minutes to raise the temperature of 0.5 kg water by 40 K. This heater is replaced by a new heater having two wires of the same material, each of length L and diameter 2d. The way these wires are connected is given in the options. How much time in minutes will it take to raise the temperature of the same amount of water by 40 K?

• A. 4 if wires are in parallel
• B. 2 if wires are in series
• C. 1 if wires are in series
• D. 0.5 if wires are in parallel

Answer 1

Answer: (B), (D)

The correct options are
B 2 if wires are in series
D 0.5 if wires are in parallel

Joules law,

$H=I^{2}Rt=\frac{V^{2}t}{R}$

Also,

$R=\rho \frac{l}{A}\Rightarrow R\propto \frac{1}{A}\Rightarrow R\propto \frac{1}{r^2}$

$\therefore R^{\prime }=\frac{R}{4}$

$parallel\Rightarrow R_p=(\frac{1}{R/4}+\frac{1}{R/4}{)}^{-1}=\frac{R}{8}$

$series\Rightarrow R_s=\frac{R}{4}+\frac{R}{4}=\frac{R}{2}$

$\therefore \frac{V^{2}4}{R}=\frac{V^2{t}_p}{R_p}=\frac{V^2{t}_s}{R_s}$

$\Rightarrow t_p=0.5min,t_s=2min$