---
title: "Two identical real batteries, each having electromotive force \\(\\mathcal{E}\\) and internal resistance \\(r\\), are connected in parallel with each other. This parallel combination is then connected across a variable load resistor of resistance \\(R_L\\). Which of the following correctly gives the terminal voltage \\(V_T\\) across the load resistor and describes how the overall power efficiency \\(\\eta = P_{\\text{load}} / P_{\\text{total}}\\)"
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url: "https://nerd-notes.com/ubq/118469/"
date_modified: "2026-08-04T08:10:27+00:00"
---

# Two identical real batteries, each having electromotive force \(\mathcal{E}\) and internal resistance \(r\), are connected in parallel with each other. This parallel combination is then connected across a variable load resistor of resistance \(R_L\). Which of the following correctly gives the terminal voltage \(V_T\) across the load resistor and describes how the overall power efficiency \(\eta = P_{\text{load}} / P_{\text{total}}\)

Two identical real batteries, each having electromotive force \(\mathcal{E}\) and internal resistance \(r\), are connected in parallel with each other. This parallel combination is then connected across a variable load resistor of resistance \(R_L\). Which of the following correctly gives the terminal voltage \(V_T\) across the load resistor and describes how the overall power efficiency \(\eta = P_{\text{load}} / P_{\text{total}}\)

![A schematic of a multi-loop circuit on a white background. At the top left, a vertical branch contains a battery represented by a long-short parallel line symbol labeled \varepsilon with positive terminal up, in series with a resistor symbol labeled r. At the middle left, a second vertical branch parallel to the first contains an identical battery symbol labeled \varepsilon with positive terminal up, in series with a resistor symbol labeled r. These two parallel branches merge at top and bottom junction nodes into a main loop. On the right vertical side of the main loop, a single resistor symbol is drawn and labeled R_L. Solid black wire lines connect all elements in a closed rectangular loop with two parallel internal battery branches on the left. No other labels, text, or arrows appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-circuit-1-1785831026-kciUDs.jpg)

- **A.** Terminal Voltage: \(V_T = \dfrac{\mathcal{E} R_L}{r + R_L}\) | Efficiency Trend: Increases as \(R_L\) increases
- **B.** Terminal Voltage: \(V_T = \dfrac{2\mathcal{E} R_L}{r + 2R_L}\) | Efficiency Trend: Increases as \(R_L\) increases
- **C.** Terminal Voltage: \(V_T = \dfrac{2\mathcal{E} R_L}{r + 2R_L}\) | Efficiency Trend: Decreases as \(R_L\) increases
- **D.** Terminal Voltage: \(V_T = \dfrac{\mathcal{E} R_L}{2r + R_L}\) | Efficiency Trend: Remains constant as \(R_L\) increases

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118469/*