Question:
When two identical batteries of internal resistance 1 Ω each are connected in series across a resistor R, the rate of heat produced in R is P1. When the same batteries are connected in parallel across R, the rate of heat produced is P2. If P1 = 2P2, then the value of R is
When two identical batteries of internal resistance 1 Ω each are connected in series across a resistor R, the rate of heat produced in R is P1. When the same batteries are connected in parallel across R, the rate of heat produced is P2. If P1 = 2P2, then the value of R is
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Remember that the rate of heat produced in a resistor depends on the square of the voltage across it and the resistance.
Updated On: Jun 6, 2025
- 4 Ω
- 10 Ω
- 5 Ω
- 2 Ω
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The Correct Option is C
Solution and Explanation
When the batteries are in series, the total resistance is the sum of their internal resistances. When they are in parallel, the effective resistance is reduced. By applying the formula for heat produced, $P = \frac{V^2}{R}$, and using the given condition $P_1 = 2P_2$, we can calculate that $R = 5 \, \Omega$.
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