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AP Physics 2
11.7 Kirchhoff’s Junction Rule
11.5 Compound Direct Current (DC) Circuits
AdvancedMCQMathematicalConceptual25.3k
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.
Circuit schematic showing parallel branches and sub-network.
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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