# Ohm's law

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## Introduction

The study of electrical circuits is essential to understand the technology that uses electricity in the real-world. This includes electricity being used for the operation of electronic devices like computers.

## Experiment : ohm's law

Aim:

In this experiment we will look at the relationship between the current going through a resistor and the potential difference (voltage) across the same resistor.

Method:

1. Set up the circuit according to the circuit diagram, starting with just one cell.
2. Draw the following table in your lab book.
 Voltage, $V$ (V) Current, $I$ (A) 1,5 3,0 4,5 6,0
3. Get your teacher to check the circuit before turning the power on.
4. Measure the current.
5. Add one more 1,5 V cell to the circuit and measure the current again.
6. Repeat until you have four cells and you have completed your table.
7. Draw a graph of voltage versus current.

Results:

1. Does your experimental results verify Ohm's Law? Explain.
2. How would you go about finding the resistance of an unknown resistor using only a power supply, a voltmeter and a known resistor ${R}_{0}$ ?

## Activity : ohm's law

If you do not have access to the equipment necessary for the Ohm's Law experiment, you can do this activity.

 Voltage, $V$ (V) Current, $I$ (A) 3,0 0,4 6,0 0,8 9,0 1,2 12,0 1,6
1. Plot a graph of voltage (on the $x$ -axis) and current (on the $y$ -axis).

Conclusions:

1. What type of graph do you obtain (straight line, parabola, other curve)
2. Calculate the gradient of the graph.
3. Do your experimental results verify Ohm's Law? Explain.
4. How would you go about finding the resistance of an unknown resistor using only a power supply, a voltmeter and a known resistor ${R}_{0}$ ?

An important relationship between the current, voltage and resistance in a circuit was discovered by Georg Simon Ohm and is called Ohm's Law .

Ohm's Law

The amount of electric current through a metal conductor, at a constant temperature, in a circuit is proportional to the voltage across the conductor. Mathematically, Ohm's Law is written:

$V=R·I.$

Ohm's Law tells us that if a conductor is at a constant temperature, the current flowing through the conductor is proportional to the voltage across it. This means that if we plot voltage on the $x$ -axis of a graph and current on the $y$ -axis of the graph, we will get a straight-line. The gradient of the straight-line graph is related to the resistance of the conductor.

## Ohmic and non-ohmic conductors

As you have seen, there is a mention of constant temperature when we talk about Ohm's Law. This is because the resistance of some conductors changes as their temperature changes. These types of conductors are called non-ohmic conductors, because they do not obey Ohm's Law. As can be expected, the conductors that obey Ohm's Law are called ohmic conductors. A light bulb is a common example of a non-ohmic conductor. Nichrome wire is an ohmic conductor.

In a light bulb, the resistance of the filament wire will increase dramatically as it warms from room temperature to operating temperature. If we increase the supply voltage in a real lamp circuit, the resulting increase in current causes the filament to increase in temperature, which increases its resistance. This effectively limits the increase in current. In this case, voltage and current do not obey Ohm's Law.

The phenomenon of resistance changing with variations in temperature is one shared by almost all metals, of which most wires are made. For most applications, these changes in resistance are small enough to be ignored. In the application of metal lamp filaments, which increase a lot in temperature (up to about 1000 ${}^{\circ }$ C, and starting from room temperature) the change is quite large.

In general non-ohmic conductors have plots of voltage against current that are curved, indicating that the resistance is not constant over all values of voltage and current.

## Experiment : ohmic and non-ohmic conductors

Repeat the experiment as decribed in the previous section. In this case use a light bulb as a resistor. Compare your results to the ohmic resistor.

## Using ohm's law

We are now ready to see how Ohm's Law is used to analyse circuits.

Consider the circuit with an ohmic resistor, $R$ . If the resistor has a resistance of 5  $\Omega$ and voltage across the resistor is 5 V, then we can use Ohm's law to calculate the current flowing through the resistor.

Ohm's law is:

$V=R·I$

which can be rearranged to:

$I=\frac{V}{R}$

The current flowing through the resistor is:

$\begin{array}{ccc}\hfill I& =& \frac{V}{R}\hfill \\ & =& \frac{5\phantom{\rule{0.277778em}{0ex}}\mathrm{V}}{5\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\Omega }\hfill \\ & =& 1\phantom{\rule{0.277778em}{0ex}}\mathrm{A}\hfill \end{array}$

The resistance of the above resistor is 10  $\Omega$ and the current going through the resistor is 4 A. What is the potential difference (voltage) across the resistor?

1. It is an Ohm's Law problem. So we use the equation:

$V=R·I$
2. $\begin{array}{ccc}\hfill V& =& R·I\hfill \\ & =& \left(10\right)\left(4\right)\hfill \\ & =& 40\phantom{\rule{3.33333pt}{0ex}}V\hfill \end{array}$
3. The voltage across the resistor is 40 V.

## Ohm's law

1. Calculate the resistance of a resistor that has a potential difference of 8 V across it when a current of 2 A flows through it.
2. What current will flow through a resistor of 6  $\Omega$ when there is a potential difference of 18 V across its ends?
3. What is the voltage across a 10  $\Omega$ resistor when a current of 1,5 A flows though it?

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