Resistance of the wire is measured as $2 \Omega$ and $3 \Omega$ at $10^{\circ} \mathrm{C}$ and $30^{\circ} \mathrm{C}$ respectively. Temperature cocoefficient of resistance of the material of the wire is:

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

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

(C) $0.011^{\circ} \mathrm{C}^{-1}$

(D) $0.055^{\circ} \mathrm{C}^{-1}$

JEE Main · 2022 · 28 Jun 2022 · Shift 2 · Current Electricity

Resistance of the wire is measured as

2Ω

and

3Ω

1 0^{\circ} C

and

3 0^{\circ} C

respectively. Temperature cocoefficient of resistance of the material of the wire is:

Answer: (A)

Using

R = R_{0} (1 + α Δ T)

3 = R_{0} (1 + 30 α)

and

2 = R_{0} (1 + 10 α)

. Dividing:

\frac{3}{2} = \frac{1 + 30 α}{1 + 10 α}

. Solving gives

α = \frac{1}{30} \approx 0.033

°C

^{- 1}

JEE Main · 2022 · 28 Jun 2022 · Shift 2 · Single correct option