Question

(a) What is the resistance of a Nichrome wire at $\mathbf{0}\mathbf{.}\mathbf{0}\mathbf{°}\mathit{C}$if its resistance is $\mathbf{100}\mathbf{.}\mathbf{00}\mathit{\Omega }$at $\mathbf{11}\mathbf{.}\mathbf{5}\mathbf{°}\mathit{C}$(b) What is the resistance of a carbon rod at $\mathbf{25}\mathbf{.}\mathbf{8}\mathbf{°}\mathit{C}$if its resistance is$\mathbf{0}\mathbf{.}\mathbf{0160}\mathit{\Omega }$ at$\mathbf{0}\mathbf{.}\mathbf{0}\mathbf{°}\mathit{C}$

Short answer

1. The resistance of Nichrome wire at$0.0°\mathrm{C}\mathrm{is}{\mathrm{R}}_0=99.5\mathrm{\Omega }$
2. The resistance of carbon rod$25.8°C$ at${\mathrm{R}}_{\mathrm{T}}=0.0158\mathrm{\Omega }$

Step-by-step solution

Determine the formula to find the resistance

Use the formula of resistance dependence temperature

Determine the resistance of a nichrome wire at 0.0°C

Use the formula found above

Thus , the resistance of nichrome wire at $0.0°C$, if its resistance is $100.00\Omega$at $11.5°C$is$99.5\Omega$

Determine the resistance of carbon rod at 25.8°C

Use the formula of resistance dependence temperature

Substitute the values

Here, $\infty$is negative because as the temperature increases, the resistance of the carbon rod decreases.

Therefore, the resistance of carbon rod at $25.8°C$, if its resistance is $0.0160\Omega$at$0.0°C$is role="math" localid="1664188564459" $0.0158\Omega$