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 40K?JEE Advanced 2014 (Paper 1)A4 if wires are in parallelB2 if wires are in seriesC1 if wires are in seriesD0.5 if wires are in parallel.
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 40K?JEE Advanced 2014 (Paper 1)A4 if wires are in parallelB2 if wires are in seriesC1 if wires are in seriesD0.5 if wires are in parallel.
Solution
The answer to this question depends on how the wires are connected in the new heater.
If the wires are connected in parallel, the total resistance of the heater will be halved. This is because the resistance of each wire is inversely proportional to its cross-sectional area (which is proportional to the square of the diameter), and when resistors are connected in parallel, the total resistance is less than the resistance of any single resistor. Therefore, the power of the heater, which is inversely proportional to the resistance, will be doubled. Since the power is the rate of energy transfer, doubling the power means that the time taken to raise the temperature of the water by 40K will be halved. So, the answer is D: 0.5 if wires are in parallel.
If the wires are connected in series, the total resistance of the heater will be the same as the original heater. This is because the resistance of each wire is inversely proportional to its cross-sectional area, and when resistors are connected in series, the total resistance is the sum of the resistances of each resistor. Therefore, the power of the heater, and hence the time taken to raise the temperature of the water by 40K, will remain the same. So, the answer is A: 4 if wires are in series.
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