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Chapter 25: Problem 21

Should light bulbs (ordinary incandescent bulbs with tungsten filaments) be considered ohmic resistors? Why or why not? How would this be determined experimentally?

Short Answer

Expert verified
Provide reasoning for your answer and describe a method to determine this experimentally. Incandescent light bulbs cannot be considered as ohmic resistors because their resistance changes with the applied voltage and temperature. This non-linear behavior is illustrated by a curved voltage-current (V-I) graph, as opposed to the linear graph observed for ohmic resistors. To determine this experimentally, a V-I graph can be plotted using data collected from a simple electrical circuit containing a light bulb connected to a variable power source (like a rheostat), an ammeter to measure the current, and a voltmeter to measure the voltage across the light bulb. Gradually increasing the voltage applied to the light bulb and observing how the current changes can help us analyze whether the light bulb exhibits ohmic behavior by evaluating the linearity of the V-I graph. Since incandescent light bulbs with tungsten filaments show a non-linear relationship between voltage and current, they cannot be considered ohmic resistors.

Step by step solution

01

Understanding Ohmic Resistors

Ohmic resistors are materials or devices that obey Ohm's law, which states that the current (I) passing through the resistor is directly proportional to the voltage (V) across it, and inversely proportional to its resistance (R). Mathematically, Ohm's law is expressed as: V = IR For a resistor to be considered ohmic, its resistance (R) should remain constant as the voltage across its terminals varies. Ohmic materials typically have a linear relationship between the voltage and current, as shown by a straight line on a V-I graph, and they maintain a constant resistance over the full range of voltages.
02

Comparing Light Bulbs with Ohmic Resistors

In an incandescent light bulb, the electric current passes through a thin tungsten filament, which heats up and emits light. As the temperature of the filament increases, the resistance of the tungsten filament also increases. This behavior is different from that of an ohmic resistor because the resistance does not remain constant as the voltage and current change. In fact, the relationship between voltage and current for a tungsten filament bulb is non-linear. When plotted on a V-I graph, it does not show a straight line as in the case of ohmic resistors. Rather, it has a slightly curved shape, indicating that the resistance changes with changes in applied voltage and temperature.
03

Experimentally Determining Ohmic Behavior

To determine experimentally whether incandescent light bulbs exhibit ohmic behavior, the following setup can be used: 1. Connect an incandescent light bulb in a simple electrical circuit with a variable power source (like a rheostat), an ammeter to measure the current, and a voltmeter to measure the voltage across the light bulb. 2. Gradually increase the voltage applied to the light bulb using the variable power source and observe how the current passing through it changes. At each voltage level, record the readings of both the ammeter and voltmeter. 3. Plot the voltage (V) on the x-axis and the current (I) on the y-axis of a graph using the collected data points. 4. Analyze the V-I graph. If the graph is linear (a straight line), then the light bulb would be considered an ohmic resistor. However, if the graph shows a non-linear (curved) relationship between voltage and current, then the light bulb cannot be considered an ohmic resistor.
04

Conclusion

Incandescent light bulbs with tungsten filaments do not exhibit ohmic behavior as their resistance changes with the applied voltage and temperature. This non-linear behavior is illustrated by a curved V-I graph, as opposed to the linear graph observed for ohmic resistors. To determine this experimentally, a V-I graph can be plotted using data collected from a simple electrical circuit containing a light bulb and variable power source, allowing for a visual comparison with the characteristics of an ohmic resistor.

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Most popular questions from this chapter

A rectangular wafer of pure silicon, with resistivity \(\rho=2300 \Omega \mathrm{m},\) measures \(2.00 \mathrm{~cm}\) by \(3.00 \mathrm{~cm}\) by \(0.010 \mathrm{~cm}\) Find the maximum resistance of this rectangular wafer between any two faces.

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