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title: "Two resistors, Resistor 1 with resistance \\(R_1 = R\\) and Resistor 2 with resistance \\(R_2 = 3R\\), are connected in parallel across an ideal battery of potential difference \\(V_0\\). The current through Resistor 1 is \\(I_1\\) and the current through Resistor 2 is \\(I_2\\). Which of the following correctly states the ratio of the currents \\(\\dfrac{I_1}{I_2}\\) and provides the correct physical justification?"
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url: "https://nerd-notes.com/ubq/118363/"
date_modified: "2026-08-04T08:09:41+00:00"
---

# Two resistors, Resistor 1 with resistance \(R_1 = R\) and Resistor 2 with resistance \(R_2 = 3R\), are connected in parallel across an ideal battery of potential difference \(V_0\). The current through Resistor 1 is \(I_1\) and the current through Resistor 2 is \(I_2\). Which of the following correctly states the ratio of the currents \(\dfrac{I_1}{I_2}\) and provides the correct physical justification?

Two resistors, Resistor 1 with resistance \(R_1 = R\) and Resistor 2 with resistance \(R_2 = 3R\), are connected in parallel across an ideal battery of potential difference \(V_0\). The current through Resistor 1 is \(I_1\) and the current through Resistor 2 is \(I_2\). Which of the following correctly states the ratio of the currents \(\dfrac{I_1}{I_2}\) and provides the correct physical justification?

![A simple circuit diagram showing an ideal battery on the left side connected to two parallel branches on the right. The top branch contains Resistor 1 with resistance labeled R and current arrow labeled I_1 pointing right. The bottom branch contains Resistor 2 with resistance labeled 3R and current arrow labeled I_2 pointing right. Both branches connect at junction nodes before returning to the battery. No other labels, lines, or components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830981-IMoiZs.jpg)

- **A.** The ratio \(\dfrac{I_1}{I_2}\) is \(\dfrac{1}{3}\), because current is directly proportional to resistance for a given potential difference.
- **B.** The ratio \(\dfrac{I_1}{I_2}\) is \(\dfrac{1}{3}\), because the current splits such that larger resistance receives a smaller fraction of the total potential difference.
- **C.** The ratio \(\dfrac{I_1}{I_2}\) is \(3\), because parallel branches experience the same potential difference.
- **D.** The ratio \(\dfrac{I_1}{I_2}\) is \(3\), because the total potential difference from the battery splits in proportion to the resistance of each branch.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118363/*