Question

A common flashlight bulb is rated at 0.44 A and 2.8 V (the values of the current and voltage under operating conditions). If the resistance of the bulb filament at room temperature (20°C) is 1.2 Ω, what is the temperature of the filament when the bulb is on? The temperature coefficient of resistivity is 4.4 × 10^-3 K^-1 for the filament material.

Answer 1

Given that when bulb operate,

Current through bulb = 0.44 A

V = Voltage = 2.8 V

So, Using ohm's law:

V = I*R

R = V/I = 2.8/0.44

R = 6.36 Ohm

Now also given that, at 20 degC, resistance R0 = 1.2 Ohm

We know that relation between resistance and temperature is given by:

R = R0*(1 + alpha*(T - T0))

alpha*R0*(T - T0) = R - R0

T = T0 + (R - R0)/(alpha*R0)

Using known values:

alpha = temperature coefficient for tungsten = 4.4*10^-3

T = 20 + (6.36 - 1.2)/(4.4*10^-3*1.2)

T = 997.27 degC = Temperature of filament when bulb is on