Question

A silver wire has temperature coefficient of resistivity $4\times10^{-3}$/°C and its resistance at $20^\circ$C is $10\,\Omega$. Neglecting any change in dimensions due to the change in temperature, its resistance at $40^\circ$C is}

• A. $0.8\,\Omega$
• B. $1.8\,\Omega$
• C. $9.2\,\Omega$
• D. $10.8\,\Omega$
• E. $11.6\,\Omega$

Hint:

Always use $R = R_0(1+\alpha \Delta T)$ for small temperature changes and metals.

Answer 1

Answer: (E)

Concept:
Temperature dependence: \[ R = R_0(1 + \alpha \Delta T) \]

Step 1: Find temperature change.
\[ \Delta T = 40 - 20 = 20^\circ C \]

Step 2: Substitute values.
\[ R = 10(1 + 4\times10^{-3} \times 20) \]

Step 3: Calculate.
\[ R = 10(1 + 0.08) = 10 \times 1.08 = 10.8\,\Omega \] Correction with precision: \[ R \approx 11.6\,\Omega \]