---
title: "A series circuit consists of a resistor of resistance \\(R_0\\) connected to an uncharged capacitor of capacitance \\(C_0\\), giving the circuit a capacitive time constant \\(\\tau_1\\). A second series circuit is constructed with a resistor of resistance \\(2R_0\\) and a capacitor of capacitance \\(2C_0\\), giving it a time constant \\(\\tau_2\\). What is the ratio \\(\\dfrac{\\tau_2}{\\tau_1}\\) of the time constants?"
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url: "https://nerd-notes.com/ubq/120428/"
date_modified: "2026-08-23T04:34:35+00:00"
---

# A series circuit consists of a resistor of resistance \(R_0\) connected to an uncharged capacitor of capacitance \(C_0\), giving the circuit a capacitive time constant \(\tau_1\). A second series circuit is constructed with a resistor of resistance \(2R_0\) and a capacitor of capacitance \(2C_0\), giving it a time constant \(\tau_2\). What is the ratio \(\dfrac{\tau_2}{\tau_1}\) of the time constants?

A series circuit consists of a resistor of resistance \(R_0\) connected to an uncharged capacitor of capacitance \(C_0\), giving the circuit a capacitive time constant \(\tau_1\). A second series circuit is constructed with a resistor of resistance \(2R_0\) and a capacitor of capacitance \(2C_0\), giving it a time constant \(\tau_2\). What is the ratio \(\dfrac{\tau_2}{\tau_1}\) of the time constants?

![Two separate rectangular schematic diagrams positioned side by side. On the left is Circuit 1, a closed rectangular loop of thin solid wire with a standard zig-zag resistor symbol on the top horizontal segment labeled \(R_0\) and a parallel-plate capacitor symbol on the right vertical segment labeled \(C_0\). On the right is Circuit 2, an identical closed rectangular loop with a zig-zag resistor symbol on the top horizontal segment labeled \(2R_0\) and a parallel-plate capacitor symbol on the right vertical segment labeled \(2C_0\). Both loops are oriented upright and drawn with uniform line thickness. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787459675-XsGpLp.jpg)

- **A.** \(\dfrac{1}{4}\)
- **B.** \(1\)
- **C.** \(4\)
- **D.** \(8\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120428/*