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title: "Two identical capacitors, each of capacitance \\(C\\), are individually charged so that the potential difference across each capacitor is \\(V_0\\). In Scenario 1, the two capacitors are connected in series with a resistor of resistance \\(R\\) to form a discharging circuit. In Scenario 2, the same two charged capacitors are connected in parallel with the same resistor \\(R\\). Let \\(\\tau_1\\) and \\(\\tau_2\\) be the circuit time constants, and let \\(I_1\\) and \\(I_2\\) be the initial discharging currents through the resistor immediately after the circuit is closed in Scenario 1 and Scenario 2, respectively. Which of the following correctly pairs the ratio \\(\\dfrac{\\tau_2}{\\tau_1}\\) of the circuit time constants and the ratio \\(\\dfrac{I_2}{I_1}\\) of the initial discharging currents?"
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url: "https://nerd-notes.com/ubq/118377/"
date_modified: "2026-08-04T08:09:47+00:00"
---

# Two identical capacitors, each of capacitance \(C\), are individually charged so that the potential difference across each capacitor is \(V_0\). In Scenario 1, the two capacitors are connected in series with a resistor of resistance \(R\) to form a discharging circuit. In Scenario 2, the same two charged capacitors are connected in parallel with the same resistor \(R\). Let \(\tau_1\) and \(\tau_2\) be the circuit time constants, and let \(I_1\) and \(I_2\) be the initial discharging currents through the resistor immediately after the circuit is closed in Scenario 1 and Scenario 2, respectively. Which of the following correctly pairs the ratio \(\dfrac{\tau_2}{\tau_1}\) of the circuit time constants and the ratio \(\dfrac{I_2}{I_1}\) of the initial discharging currents?

Two identical capacitors, each of capacitance \(C\), are individually charged so that the potential difference across each capacitor is \(V_0\). In Scenario 1, the two capacitors are connected in series with a resistor of resistance \(R\) to form a discharging circuit. In Scenario 2, the same two charged capacitors are connected in parallel with the same resistor \(R\). Let \(\tau_1\) and \(\tau_2\) be the circuit time constants, and let \(I_1\) and \(I_2\) be the initial discharging currents through the resistor immediately after the circuit is closed in Scenario 1 and Scenario 2, respectively. Which of the following correctly pairs the ratio \(\dfrac{\tau_2}{\tau_1}\) of the circuit time constants and the ratio \(\dfrac{I_2}{I_1}\) of the initial discharging currents?

- **A.** \(\dfrac{\tau_2}{\tau_1} = \dfrac{1}{4}\) and \(\dfrac{I_2}{I_1} = 2\)
- **B.** \(\dfrac{\tau_2}{\tau_1} = 1\) and \(\dfrac{I_2}{I_1} = \dfrac{1}{2}\)
- **C.** \(\dfrac{\tau_2}{\tau_1} = 4\) and \(\dfrac{I_2}{I_1} = 2\)
- **D.** \(\dfrac{\tau_2}{\tau_1} = 4\) and \(\dfrac{I_2}{I_1} = \dfrac{1}{2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118377/*