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Sunday, January 29, 2023

Topic 2 Ohm’s Law

Resistance is the ratio of the voltage to the current, described in the simple equation R = V/I.  In a metallic conductor, we find that if we alter the voltage or the current, the other variable changes in such a way that the ratio remains constant.

 R = V  Learn this for the exam I

This is Ohm’s Law, which states:

The current in a metallic conductor is directly proportional to the potential difference between its ends provided that the temperature and other physical conditions are the same.

A conductor that obeys Ohm’s Law is called an ohmic conductor.

Question 1  What are the key points to Ohm’s Law?

Voltage Current Characteristics

We can easily measure voltage and current, using the data to plot voltage current graphs.  We use the following circuit, which you probably did in Year 10 (the 4th Year):

From this circuit we take readings of voltage and current plotting them as a graph called a VI characteristic.

We normally put the voltage on the y-axis and current on the x-axis.  This allows us to determine the resistance from the gradientThis is a voltage current graph for an ohmic conductor:

The straight line shows a constant ratio between voltage and current, for both positive and negative values.  So when the voltage is negative, the current is negative, i.e. flowing in the opposite direction.  Ohm’s Law is obeyed.

For a filament lamp we see:

The resistance rises as the filament gets hotter, which is shown by the gradient getting steeper.

Question 2  Can you explain why the shape of this graph suggests that a light bulb does not obey Ohm’s Law?

thermistor (a heat sensitive resistor) behaves in the opposite way.  Its resistance goes down as it gets hotter.  This is because the material releases more electrons to be able to conduct.  Don’t worry about why this happens; it’s not on the syllabus.  If you really want to know,

Although it looks similar to the graph above, notice how the gradient is decreasing, indicating a lower resistance.  There is, however, a health warning:

• As the current goes up, the thermistor gets hotter.
• As it gets hotter, it allows more current to flow;
• Therefore it gets hotter and so on.

This is called thermal runaway, and is a feature of many semi-conductor components.  At the extreme the component will glow red-hot, then split apart.   I know, I have done it.  Do NOT try it for yourself (unless you want an earful from your physics teacher, and possibly an interview with the vice-principal).

The thermistor is used wherever any electronic circuit detects temperature:

Here we see a thermistor protecting a power supply from too high a temperature.

Question 3  Why does a thermistor not obey Ohm’s Law?

You can investigate how temperature and resistance are related in a thermistor using equipment like this:

Diodes are semi-conductor devices that allow electric current to flow one way only.

The diode characteristic graph looks like this:

Note the way it is presented.  I have done it like this to be consistent with all the other characteristic graphs.  However many text books show the graph with the voltage on the horizontal axis and current on the vertical.  Watch out for this bear-trap in the exam.

The diode starts to conduct at a voltage of about +0.6 V.  We call this forward bias.  Then the current rises rapidly for a small rise in voltage. If the current is reversed (reverse bias) almost no current flows until the breakdown voltage is reached.  This usually results in destruction of the diode.

Question 4  (Harder) Can you use the graph to explain why a diodes allows a current to flow one way only?

Resistivity

The resistance of a wire depends on three factors:

• the length; double the length, the resistance doubles.
• the area; double the area, the resistance halves.
• the material that the wire is made of.

Resistivity is a property of the material.  It is defined as the resistance of a wire of the material of unit area and unit length.

The formula for resistivity is:

In physics code we write this as r = AR/l

 r = AR  learn this for the exam l

There are three bear traps

• The unit for resistivity is ohm metre (Wm), NOT ohms per metre.
• Notice too that the physics code r (rho, a greek letter ‘r’) is the same as that for density.  Resistivity has NOTHING to do with density.
• The area is in square metres.  Real wires have areas in square millimetres; 1 mm2 = 1 x 10-6 m2

Question 5 Constantan has a resistivity of 47 ´ 10-8 Wm.  How much of this wire is needed to make a 10 ohm resistor, if the diameter is 0.5 mm?

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