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title: "A cylindrical resistor of length \\(L\\) and diameter \\(D\\) is connected across an ideal power supply providing a constant potential difference \\(V_0\\), dissipating thermal energy at a rate \\(P_0\\). The resistor is replaced with a second cylindrical resistor of the same material and length \\(L\\), but with diameter \\(\\dfrac{D}{2}\\), connected across the same potential difference \\(V_0\\). What is the ratio of the power dissipated in the second resistor to the power dissipated in the first resistor, \\(\\dfrac{P_2}{P_0}\\)?"
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url: "https://nerd-notes.com/ubq/121539/"
date_modified: "2026-08-23T05:23:50+00:00"
---

# A cylindrical resistor of length \(L\) and diameter \(D\) is connected across an ideal power supply providing a constant potential difference \(V_0\), dissipating thermal energy at a rate \(P_0\). The resistor is replaced with a second cylindrical resistor of the same material and length \(L\), but with diameter \(\dfrac{D}{2}\), connected across the same potential difference \(V_0\). What is the ratio of the power dissipated in the second resistor to the power dissipated in the first resistor, \(\dfrac{P_2}{P_0}\)?

A cylindrical resistor of length \(L\) and diameter \(D\) is connected across an ideal power supply providing a constant potential difference \(V_0\), dissipating thermal energy at a rate \(P_0\). The resistor is replaced with a second cylindrical resistor of the same material and length \(L\), but with diameter \(\dfrac{D}{2}\), connected across the same potential difference \(V_0\). What is the ratio of the power dissipated in the second resistor to the power dissipated in the first resistor, \(\dfrac{P_2}{P_0}\)?

- **A.** \(\dfrac{1}{4}\)
- **B.** \(\dfrac{1}{2}\)
- **C.** \(2\)
- **D.** \(4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121539/*