The resistance of a conductor at $15^{\circ} \mathrm{C}$ is $16 \Omega$ and at $100^{\circ} \mathrm{C}$ is $20 \Omega$. What will be the temperature coefficient of resistance of the conductor ?

(A) $0.003^{\circ} \mathrm{C}^{-1}$

(B) $0.042^{\circ} \mathrm{C}^{-1}$

(C) $0.033^{\circ} \mathrm{C}^{-1}$

(D) $0.010^{\circ} \mathrm{C}^{-1}$

JEE Main · 2021 · 27 Jul 2021 · Shift 2 · Current Electricity

The resistance of a conductor at

1 5^{\circ} C

16Ω

and at

10 0^{\circ} C

20Ω

. What will be the temperature coefficient of resistance of the conductor ?

Answer: (A)

Resistance varies with temperature as

R_{t} = R_{0} (1 + α t)

, the coefficient being referred to

0^{\circ}

C. Taking the ratio of the two measurements removes

R_{0}

\frac{1 + 100 α}{1 + 15 α} = \frac{20}{16}

16 (1 + 100 α) = 20 (1 + 15 α)

16 + 1600 α = 20 + 300 α \Rightarrow 1300 α = 4

α = \frac{4}{1300} = 3.1 \times 1 0^{- 3}^{\circ} C^{- 1}

The temperature coefficient of resistance of the conductor is

0.003^{\circ} C^{- 1}

JEE Main · 2021 · 27 Jul 2021 · Shift 2 · Single correct option