## Related questions with answers

(a) What is the resistance of a Nichrome wire at $0.0^{\circ} \mathrm{C}$ if its resistance is $100.00 \Omega$ at $11.5^{\circ} \mathrm{C}$ ? (b) What is the resistance of a carbon rod at $25.8^{\circ} \mathrm{C}$ if its resistance is $0.0160 \Omega$ at $0.0^{\circ} \mathrm{C}$ ?

Solution

Verified$\textbf{a)}$ \ \ Resistivity of a material varies with temperature, the resistance of a specific conductor also varies with temperature. For temperature ranges that are not too great, this variation is approximately a linear relationship described with expression below:

$\begin{equation*} R = R_0 \cdot [1 + \alpha \cdot (T - T_0)] \end{equation*}$

$\alpha$ is temperature coefficient of resistance, for Nichrome this will be:

$\begin{equation*} \alpha_{nichrome} = 0.0004 \ [^oC^{-1}] \end{equation*}$

If resistance of Nichrome wire at $T = 11.5 \ ^oC$ is $R= 100.00 \ \Omega$, at temperature of $T_0 = 0.0 \ ^oC$ the resistance $R_0$ will be:

$\begin{align*} &R = R_0 \cdot [1 + \alpha \cdot (T - T_0)] \\ \\ \implies &R_0 = \frac{R}{1 + \alpha \cdot (T - T_0)} \\ \\ &R_0 = \frac{100.00 \ \Omega}{1 + 0.0004 \ ^oC^{-1} \cdot (11.5 \ ^oC - 0 ^oC)} \\ \end{align*}$

$\begin{equation*} \boxed{R_0 = 99.542 \ \Omega} \end{equation*}$

## Create an account to view solutions

## Create an account to view solutions

## More related questions

1/4

1/7