Physics

Physics

Problem

Two resistors R1R_1 and R2R_2 are connected one at a time across the same battery. If R1<R2R_1 < R_2, which statement about the power dissipated is correct? a) Power in R1R_{1} equals power in R2R_{2} b) Power depends only on the voltage, not on resistance c) Power in R1R_{1} is greater than in R2R_{2} d) Power in R1R_{1} is less than in R2R_{2}
Intuitive explanation

The key insight is that power depends on both resistance and voltage—but here the voltage stays constant (same battery), so you're really comparing how current changes. Since P=V2/RP = V^2/R, a smaller resistance lets more current flow and dissipates more power from the battery. Think of it this way: lower resistance is like a wider pipe, allowing the battery to "push" more energy per second through the circuit.

Intuitive explanation

The key insight is that power depends on both resistance and voltage—but here the voltage stays constant (same battery), so you're really comparing how current changes. Since P=V2/RP = V^2/R, a smaller resistance lets more current flow and dissipates more power from the battery. Think of it this way: lower resistance is like a wider pipe, allowing the battery to "push" more energy per second through the circuit.

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