Question 26.21: A common flashlight bulb is rated at 0.30 A and 2.9 V (the v......
A common flashlight bulb is rated at 0.30 A and 2.9 V (the values of the current and voltage under operating conditions). If the resistance of the tungsten bulb filament at room temperature (20°C) is 1.1 Ω, what is the temperature of the filament when the bulb is on?
The resistance at operating temperature T is R = V/i = 2.9 V/0.30 A = 9.67 Ω. Thus, from R-R_0=R_0 \alpha\left(T-T_0\right) , we find
T=T_0+\frac{1}{\alpha}\left(\frac{R}{R_0}-1\right)=20^{\circ} C +\left(\frac{1}{4.5 \times 10^{-3} / K }\right)\left(\frac{9.67 \,\Omega}{1.1 \,\Omega}-1\right)=1.8 \times 10^3{ }^{\circ}C .
Since a change in Celsius is equivalent to a change on the Kelvin temperature scale, the value of α used in this calculation is not inconsistent with the other units involved. Table 26-1 has been used.
| Table 26-1 Resistivities of Some Materials at Room Temperature (20°C) | ||
| Material | Resistivity, ρ ( Ω·m) | Temperature Coefficient of Resistivity, α (K^{-1}) |
| Typical Metals | ||
| Silver | 1.62 \times 10^{-8} | 4.1 \times 10^{-3} |
| Copper | 1.69 \times 10^{-8} | 4.3 \times 10^{-3} |
| Gold | 2.35 \times 10^{-8} | 4.0 \times 10^{-3} |
| Aluminum | 2.75 \times 10^{-8} | 4.4 \times 10^{-3} |
| Manganin ^a | 4.82 \times 10^{-8} | 0.002 \times 10^{-3} |
| Tungsten | 5.25 \times 10^{-8} | 4.5 \times 10^{-3} |
| Iron | 9.68 \times 10^{-8} | 6.5 \times 10^{-3} |
| Platinum | 10.6 \times 10^{-8} | 3.9 \times 10^{-3} |
| Typical Semiconductors | ||
| Silicon, pure | 2.5 \times 10^3 | -70 \times 10^{-3} |
| Silicon, n-type^b | 8.7 \times 10^{-4} | |
| Silicon,p-type^c | 2.8 \times 10^{-3} | |
| Typical Insulators | ||
| Glass | 10^{10}-10^{14} | |
| Fused | ||
| quartz | \sim 10^{16} | |
| ^a An alloy specifically designed to have a small value ofα. | ||
| ^bPure silicon doped with phosphorus impurities to a charge carrier density of 10^{23} m^{-3}. | ||
| ^cPure silicon doped with aluminum impurities to a charge carrier density of 10^{23} m^{-3}. | ||