Chapter 18, Problem 83GP

To determine

The temperature of the filament when the flash light is ON.

Answer to Problem 83GP

  $2200°C$

Explanation of Solution

Given:

Original temperature is $20°C$ .

Resistance of tungsten filament at $20°C$ is $1.5\Omega$ .

Current, $I=0.20A$

Voltage, $V=3.2V$

Formula used:

The resistivity of metal increases linearly with the temperature. Expression for this: ${\rho }_T={\rho }_0\left[1+\alpha \left(T-T_0\right)\right]$

Where,

  ${\rho }_0$ is the resistivity at reference temp $T_0$ ,

  ${\rho }_T$ is the resistivity at reference temp $T$ ,

  $\alpha$ is the temperature coefficient of resistance.

Calculation:

Resistance, $R=\frac{V}{I}=\frac{3.2}{0.20}=16\Omega$

By using the formula for temperature-dependent resistivity, ${\rho }_T={\rho }_0\left[1+\alpha \left(T-T_0\right)\right]$ :

  $R=R_0\left[1+\alpha \left(T-T_0\right)\right]$

  $T=T_0+\frac{1}{\alpha }\left(\frac{R}{R_0}-1\right)$

Now, substitute the given equation and the temperature coefficient $\alpha$ . So,

  $=20°C+\frac{1}{\left(0.0045°C^{-1}\right)}\left(\frac{16\Omega }{1.5\Omega }-1\right)=2168°C\approx 2200°C$

Conclusion: The required temperature is $2200\text{}°C$ .