NEET 2024 — Physics solution

NEET2024Physics

Two heaters A and B have power rating of 1 kW and 2 kW, respectively. Those two are first connected in series and then in parallel to a fixed power source. The ratio of power outputs for these two cases is:

A
1 : 2
B
2 : 3
C
1 : 1
D
2 : 9

Solution

At fixed supply voltage $V$ , heater resistance $R = V^{2} / P$ , so $R_{A} = V^{2} /1000$ , $R_{B} = V^{2} /2000$ , i.e. $R_{A} : R_{B} = 2 : 1$ .

Series: $P_{s} = \frac{V ^{2}}{R _{A} + R _{B}} = \frac{V ^{2}}{3 R _{B}} = \frac{2000}{3}$ W.

Parallel: $P_{p} = P_{A} + P_{B} = 1000 + 2000 = 3000$ W.

Ratio $P_{s} : P_{p} = (2000/3) : 3000 = 2 : 9$ .

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