JEE Advanced 2014 · Paper 1 · Physics Q7

← JEE Advanced 2014 · Paper 1

PhysicsMultiple correct+3Question 7 of 60

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?

4 if wires are in parallel

2 if wires are in series

1 if wires are in series

0.5 if wires are in parallel

Answer and worked solution

Official answer: B, D

Resistances. $R=\dfrac{\rho L}{\pi d^2/4}$ . Doubling the diameter quarters the resistance, so each new wire has $R/4$ .

Time. With a fixed supply voltage, power $V^2/R_\text{eq}$ , and the time for the same heat is proportional to $R_\text{eq}$ .

Series: $R_\text{eq}=R/2$ , time $=4\times\frac12=2$ min. (B) true, (C) false.
Parallel: $R_\text{eq}=R/8$ , time $=4\times\frac18=0.5$ min. (D) true, (A) false.

(B), (D)

Topics:Electrical power and heating Ohm's law and resistivity Series and parallel resistors

← Previous question Next question →

JEE Advanced 2014 · Paper 1, Physics question 7