Resistance of a wire at 50^∘ C is 5 Ω, and at 100^∘ C it is 6 Ωfind its resistance at 0^∘ C (A)

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Resistance of a wire at 50^∘ C is 5 Ω, and at 100^∘ C it is...

Resistance of a wire at $50^{\circ} \mathrm{C}$ is $5 \Omega$, and at $100^{\circ} \mathrm{C}$ it is $6 \Omega$ find its resistance at $0^{\circ} \mathrm{C}$
(A) $4 \Omega$
(B) $3 \Omega$
(C) $2 \Omega$
(D) $1 \Omega$

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Key Concepts

Linear Temperature Dependence of Resistance

This concept refers to the relationship where the resistance of a conductor changes in a linear manner with temperature. Typically, the resistance at a given temperature can be calculated using an equation that adjusts the resistance from a known base temperature by adding a term proportional to the temperature change, assuming the linear model holds true within the temperature range in consideration.

Temperature Coefficient of Resistance

The temperature coefficient of resistance is a parameter that quantifies how much the resistance of a material changes per degree change in temperature. It is defined as the fractional change in resistance per unit temperature and is crucial for determining the resistance at different temperatures when a linear relationship is assumed.

Algebraic Manipulation of Linear Equations

To solve problems involving temperature-dependent resistance, it is often necessary to set up and solve simultaneous linear equations derived from the linear dependence equation. This allows for the determination of unknown quantities, such as the base resistance at a specific reference temperature or the coefficient of resistance.

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