The resistance of a wire is 5 Ωat 50^∘ C and 6 Ωat 100^∘ C. The resistance of the wire at 0^∘ C

Name: Problem 156, Chapter 14: A Complete Resource Book in Physics for JEE Main
Uploaded: 2021-09-28T05:07:21-08:00
Duration: 1 min 29 s
Channel: Mahipal Kumawat
Description: The resistance of a wire is 5 Ωat 50^∘ C and 6 Ωat 100^∘ C. The resistance of the wire at 0^∘ C will be (A) 2 Ω(B) 1 Ω(C) 4 Ω(D) 3 Ω

step 1 At at T degree centigrade RT resistance value is given by R0 which is resistance at 0 degree cen

Question

The resistance of a wire is $5 \Omega$ at $50^{\circ} \mathrm{C}$ and $6 \Omega$ at $100^{\circ} \mathrm{C}$. The resistance of the wire at $0^{\circ} \mathrm{C}$ will be (A) $2 \Omega$ (B) $1 \Omega$ (C) $4 \Omega$ (D) $3 \Omega$

   The resistance of a wire is $5 \Omega$ at $50^{\circ} \mathrm{C}$ and $6 \Omega$ at $100^{\circ} \mathrm{C}$. The resistance of the wire at $0^{\circ} \mathrm{C}$ will be 
(A) $2 \Omega$
(B) $1 \Omega$
(C) $4 \Omega$
(D) $3 \Omega$

A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar 1st Edition

Chapter 14, Problem 156

Instant Answer

Solved by Expert Mahipal Kumawat

09/28/2021

Step 1

Step 1: The resistance of a wire at a given temperature can be calculated using the formula: \[ R_T = R_0(1 + \alpha T) \] where $ R_T $ is the resistance at temperature $ T $, $ R_0 $ is the resistance at $ 0^{\circ}C $, and $ \alpha $ is the temperature Show more…

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The resistance of a wire is $5 \Omega$ at $50^{\circ} \mathrm{C}$ and $6 \Omega$ at $100^{\circ} \mathrm{C}$. The resistance of the wire at $0^{\circ} \mathrm{C}$ will be (A) $2 \Omega$ (B) $1 \Omega$ (C) $4 \Omega$ (D) $3 \Omega$

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Key Concepts

Linear Relationship Between Resistance and Temperature

For many conductors over moderate temperature ranges, resistance varies linearly with temperature. This relationship is often expressed in the form R = R?(1 + ??T), where R? is the resistance at a reference temperature and ?T is the change in temperature. This linear model allows for straightforward calculation of resistance at various temperatures.

Temperature Coefficient of Resistance

This concept defines how much the resistance of a material changes per degree change in temperature. It is represented by a constant (?) and indicates whether the material’s resistance increases or decreases with an increase in temperature. Understanding this coefficient is essential for predicting and calculating resistance at different temperatures.

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