---
title: "A circuit initially consists of an ideal battery of potential difference \\(\\Delta V\\) connected to a single resistor of resistance \\(R\\). An identical resistor is then connected in parallel with the first resistor, and measurements confirm that the total rate of electrical energy dissipated by the circuit doubles. Which of the following statements provides the correct physical explanation for this observation?"
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url: "https://nerd-notes.com/ubq/120434/"
date_modified: "2026-08-23T04:34:38+00:00"
---

# A circuit initially consists of an ideal battery of potential difference \(\Delta V\) connected to a single resistor of resistance \(R\). An identical resistor is then connected in parallel with the first resistor, and measurements confirm that the total rate of electrical energy dissipated by the circuit doubles. Which of the following statements provides the correct physical explanation for this observation?

A circuit initially consists of an ideal battery of potential difference \(\Delta V\) connected to a single resistor of resistance \(R\). An identical resistor is then connected in parallel with the first resistor, and measurements confirm that the total rate of electrical energy dissipated by the circuit doubles. Which of the following statements provides the correct physical explanation for this observation?

![Two side-by-side schematic circuit diagrams labeled Circuit 1 on the left and Circuit 2 on the right. In Circuit 1, a rectangular wire loop contains an ideal battery on the left vertical segment, labeled \Delta V, with a longer line above a shorter line, and a single zig-zag resistor labeled R on the right vertical segment. In Circuit 2, a rectangular wire loop contains an identical battery labeled \Delta V on the left vertical segment, a middle vertical branch containing a zig-zag resistor labeled R, and a right vertical branch containing an identical zig-zag resistor labeled R connected in parallel across the middle branch. Connecting wires in both circuits are represented by solid lines with right-angle corners. No other labels, text, arrows, or components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-circuit-diagram-1787459678-NhABi4.jpg)

- **A.** The battery delivers a fixed total current to the circuit, so adding the parallel path halves the equivalent resistance, which doubles the total power dissipated because the rate of energy dissipation is inversely proportional to resistance at constant current.
- **B.** The current from the battery divides equally between the two branches, causing the potential difference across each branch to double to maintain energy conservation, which results in twice the total rate of electrical energy dissipation.
- **C.** The battery maintains a constant potential difference across both branches, so the current through the original resistor remains unchanged while an equal current flows through the new branch, doubling the total current drawn from the battery.
- **D.** The reduced equivalent resistance causes the electric field inside each individual resistor to double, which doubles the current in each branch and quadruples the rate of energy dissipated by each individual resistor.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120434/*