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title: "A circuit is constructed with an ideal battery of potential difference \\(V_0\\) connected to two parallel branches, Branch 1 and Branch 2. Branch 1 contains a single resistor of resistance \\(R_1\\). Branch 2 contains a resistor of resistance \\(R_2\\) in series with a parallel sub-network consisting of two identical resistors, each of resistance \\(R_3\\). Let \\(I_1\\) be the current through Branch 1, and let \\(I_3\\) be the current through one of the individual resistors of resistance \\(R_3\\). Which of the following expressions correctly represents the ratio \\(\\dfrac{I_3}{I_1}\\)?"
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url: "https://nerd-notes.com/ubq/117243/"
date_modified: "2026-08-04T06:45:05+00:00"
---

# A circuit is constructed with an ideal battery of potential difference \(V_0\) connected to two parallel branches, Branch 1 and Branch 2. Branch 1 contains a single resistor of resistance \(R_1\). Branch 2 contains a resistor of resistance \(R_2\) in series with a parallel sub-network consisting of two identical resistors, each of resistance \(R_3\). Let \(I_1\) be the current through Branch 1, and let \(I_3\) be the current through one of the individual resistors of resistance \(R_3\). Which of the following expressions correctly represents the ratio \(\dfrac{I_3}{I_1}\)?

A circuit is constructed with an ideal battery of potential difference \(V_0\) connected to two parallel branches, Branch 1 and Branch 2. Branch 1 contains a single resistor of resistance \(R_1\). Branch 2 contains a resistor of resistance \(R_2\) in series with a parallel sub-network consisting of two identical resistors, each of resistance \(R_3\). Let \(I_1\) be the current through Branch 1, and let \(I_3\) be the current through one of the individual resistors of resistance \(R_3\). Which of the following expressions correctly represents the ratio \(\dfrac{I_3}{I_1}\)?

![A schematic circuit diagram showing an ideal battery labeled V_0 on the left vertical wire, positive terminal facing up. Wires extend horizontally to the right to form a parallel network with two main horizontal branches. The top branch, Branch 1, contains a single resistor labeled R_1 with a current arrow labeled I_1 pointing rightward. The bottom branch, Branch 2, contains a resistor labeled R_2 connected in series to a parallel sub-network. This sub-network splits into two parallel sub-branches, each containing a resistor labeled R_3. A current arrow labeled I_3 points rightward through the upper R_3 resistor. All branches recombine before returning to the negative terminal of the battery. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785825905-gofS9E.jpg)

- **A.** \(\dfrac{2R_1}{2R_2 + R_3}\)
- **B.** \(\dfrac{R_1}{2R_2 + R_3}\)
- **C.** \(\dfrac{R_1}{R_2 + 2R_3}\)
- **D.** \(\dfrac{2R_1}{R_2 + R_3}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117243/*