Your research team has built a device for monitoring the ozone content in the at

Question

Your research team has built a device for monitoring the ozone content in the atmosphere to determine the extent of the ozone holes over the poles. You have been assigned the job of keeping the equipment at the South Pole running during the winter months when no supplies can get in. When a piece of equipment fails, you need to replace two resistors. Unfortunately you have only one. You do have a light bulb but wonder how well a light bulb can substitute for a resistor in the circuit. You decide to make a direct comparison.

A) What is the relationship between the current through a resistor and the potential difference (voltage) across the resistor if the resistor is made of ohmic material? Draw a graph of voltage versus current for this resistor. How is the slope of the graph related to its resistance?

B) As more current goes through a light bulb, it gets brighter. As it gets brighter, it gets hotter. Do you expect the increasing temperature to affect the resistance of the bulb? If so, how?

C) Sketch a qualitative graph of voltage across a light bulb versus current through the light bulb.

Explanation / Answer

Hi,

In order to solve this problem, we should remember concepts like: Ohm's Law, resistance, electric resistivity and its relation with the temperature. Unfortunately I cannot paste the graphics from my computer, so I will try to describe them the best I can.

A) According to Ohm's Law, which is followed by many materials, the voltage and the current through an object induced by said voltage have a linear proportion and the parameter used as proportionality constant is the resistance of the object. This can be see in a better way thanks to its mathematical representation:

V = R I ; where V is the voltage, R is the resistance and I is the electric current.

Another benefit of the mathematical representation shown above is that we can predict the form of a graphic V vs I. Said graphic will be a straight line that will contain the origin and its slope will be the resistance.

Besides, if the function in the graphic is a straight line, obviously the value of its slope would be a constant.

B) According to a theory first proposed by Paul Drude, the resistance of an object is related to the temperature. In fact, in a wide range of temperatures, the relation between them is linear. However, as we come closer to very low temperatures this relation changes. Mathematically, the resistance of an object in the range whose relation with temperature is linear is:

R = Ro [1 + ( T - To) ] ; where R is the resistance of the object, Ro is the resistance of said object but measured at a reference temperature, T is the temperature, To is the reference temperature and is a parameter called temperature coefficient of resistivity.

So I do expect a change of resistance if there's a change in temperature.

C) A light bulb produces light transforming the electric energy provided by a battery into heat and light. This behavior is very similar to one of a normal resistor, as they dissipate the electrical energy into heat. So, if the material of the light bulb follows Ohm's Law I would expect a very similar graph to the one drawn in the first part.

I hope it helps.

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