Physics 153 Experiment 2 (1 week)

Tungsten Light Bulb rev. Jan. 20/09

The objective is to study a tungsten light bulb. We would like to determine the operating temperature of the bulb and the efficiency. What is provided: As shown in Figure 1 the following apparatus is provided for Lab 2:

• tungsten light bulb

• box to hold light bulb and to allow easy access to filament terminals

• two multimeters: one for the measurement of AC voltage; the other for AC current

• variac to vary the input voltage from zero to 120 VAC

• isolation transformer between variac and the light bulb to prevent electrical shock to student

• a converging lens

• a tape measure The efficiency of a lighting source is defined by

InputPowerElectrical

EmittedLightofPowerEfficiency =

Equation 1: Efficiency of Light Bulb

The electrical power input is readily obtained from measurement of the voltage and current used by the light bulb; i.e. P = I V. The power of the emitted light is a bit more difficult to obtain. We are going to deduce the emitted light power by making use of the theory for black body radiation.

Part 1: Indirect method to measure efficiency

In first term of Physics 153 we learned that the net power emitted by a black body is given by

)( 404 TTAeP −= σ

Equation 2: Total Radiative Power from Blackbody Source

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where e = emissivity, σ = Stefan’s constant = 5.67 x 10-8 W/m2 K4, A = surface of emitting body, T = temperature of body (in Kelvin), and T0 = temperature of surroundings (i.e. room temperature).

Figure 1: Apparatus for Experiment 2

The temperature dependence of the resistance of the tungsten filament is approximately given by:

)](1[)()( 00 TTTRTR −+= α

Equation 3: Resistance as Function of Temperature

Here, R(T) is the resistance at temperature T, in degrees Celsius, R(T0) is the resistance at a reference temperature usually T0 = 20°C, and α = temperature coefficient of resistivity. For tungsten α = 0.0045 °C-1. Thus, we see that by measurement of R(T) and R(T0) we can deduce T. The starting point in this lab is the measurement of R(T0). If we had a suitable ohmmeter then we could directly measure the above resistance, as shown in Figure 2. However,

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this resistance is less than one ohm, which is too low for the minimum possible resistance that can be accurately measured with our multimeter. Thus, we will use a different method to determine R(T0), as outlined below. Our multimeters can accurately measure the voltages and currents for the light bulb; thus, we can use Ohm’s law to determine R (R = V/I). However, there is a problem with this method. When we pass current through the filament, the tungsten heats up and, thereby, the resistance changes due to the above-mentioned α. Thus, the resistance that we calculate using R = V/I will be higher than R(T0). We can overcome this problem by plotting R (on y-axis) as a function of power (on x-axis) and then extrapolating to zero power. The y-intercept is R(T0). The circuit shown in Figures 3-7 can be used to measure simultaneously the voltage across the filament and the current through the filament. The voltage generator for the bulb is the 60 Hz AC power line. A Variac (figure 4) is used to vary the input voltage from zero to about 120 volts rms1. Note: the voltage to the bulb must not exceed 12 Volts rms, which corresponds to a Variac setting of about 110. Note: we want to use AC (alternating current) settings for the multimeter. >>> Deduce R(T0). Hint: Plot R as a function of P. You should have about 25-30 points up to a voltage of about 11 volts. (Remember, the voltage across the bulb is not to exceed 12 volts). Try to measure about 6-8 data points at the lower end of the curve (below about 2.5 volts) and use these to fit a linear line and, thereby, obtain the intercept, R(T0). >>> Determine the temperature as a function of electrical power, P. Plot the results. You don’t need to calculate T for every value. Every second value will be fine. To use equation 2 you will require the area, A, of the tungsten filament. But you do not have direct access to the filament; i.e. the glass enclosure is in the way. Thus, you will use a lens to project a magnified image, as shown in figure 8. In high school you learned, and in the second term of Physics 153 you will learn again, that a converging lens can be used to form a real image of a source of light. The magnification is given by M = -s’/s, where s = the distance from the source to the lens, and s’ is the distance from the lens to the image. If the image is much larger than the filament size, then we can use the simple tape measure to accurately determine the size of the image (see Figure 8) and, thereby, the filament size can be readily deduced.

1 “rms” refers to “root mean square”. An alternating source oscillates up and down with maximum

value equal to +A0 and minimum value –A0, where A0 is the amplitude for the oscillation. For a sinusoidal oscillation the rms value is equal to A0/2

1/2. Note: A multimeter set to AC settings

measures and displays the rms values (for voltage or current).

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Figure 2: Direct Measurement of Filament Resistance with Multimeter

Figure 3: Setup for Measurement of Current and Voltage

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Figure 4: Variac Used to Vary Amplitude of Input Voltage

Figure 5: Two Multimeters; one to Measure Voltage, the other to Measure Current

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Figure 6: Multimeter Used to Measure Current (Note position of knob and cables)

Figure 7: Multimeter Used to Measure Voltage (Note position of knob and cable)

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Figure 8: Optical Setup for Measurement of Filament Area

>> Deduce the area of the filament. Note: The filament is a coil; thus, you should make an approximation to simplify the calculation of the area. >> Calculate radiated power (P(rad) as a function of electrical power, P(elec). As above, every second point will give you enough values. Assume an emissivity of 0.5. For a few of the higher values of P(elec), calculate the efficiency, P(rad)/P(elec), of the tungsten filament at emitting radiation.