Ohm’s Law describes the relationship between current, voltage and resistance in an electric circuit.
Ohm’s Law states:
The current in a circuit is directly proportional to voltage and inversely proportional to resistance.
Let:
I = current
E = voltage
R = resistance
Part of Ohms Law says: current is directly proportional to voltage.
Using the symbols given, we can write an equation to show a direct proportion between current and voltage.
I = E
Normally the above equation is read I ‘equals’ E. It can just as easily and more understandably be read as: I is directly proportional to E.
I know I harp on the direct proportion and inverse proportion stuff a lot. I do so because it is so important to thoroughly understand this when we come to more complex equations.
I = E
Means that if the voltage is increased or decreased in a circuit then the current will increase or decrease by the same amount. Double the voltage and you double the current.
Halve the voltage and you halve the current. This is a direct proportion.
The other part of Ohm’s Law says that current is inversely proportional to the resistance.
This can be written as:
I = 1/R
Now 1/R is a fraction with a numerator (the top part, 1) and a denominator, R.
1/R is a fraction just like 1/4, 1/2 and 3/8 are fractions.
R is the denominator in the fraction. What happens to the whole fraction if the denominator is changed? Watch.
1/2, 1/3, 1/4, 1/5, 1/6
As the denominator increases the fraction decreases. In fact if the denominator doubles then the fraction is half the size. 1/4 is half the size of 1/2. I is the same as 1/R. This is an inverse proportion. If I is the same as 1/R and R is increased in size by three times, then the fraction 1/R is a third the size now, and since 1/R is the same as the current, then the current is a third the size also.
The complete equation for Ohm’s Law then is:
I = E/R
This equation, derived from ohms law, enables us to find the current flowing in any circuit if we know the voltage (E) and resistance (R) of the circuit.
For example: A resistor of 20 ohms has a 10 volt battery connected to across it. How much current will flow through the resistor?
I = 10/20 = 1/2 = 0.5 Amperes
The equation I = E/R can be transposed for E or for I.
In some texts a thing called the Ohm’s Law triangle is used to help you rewrite the equation for E and R – I don’t like this method, as you do really need to know how to transpose equations – not just this one. If you learn to transpose this equation then you will be able to do it with many others. There is a memory wheel on the web site for you to download that will help you remember equations for Ohm’s law and power. You will also find a tutorial on transposing equations and using a calculator in the downloads area if you feel you might need some extra help. Always write to your facilitator if you need assistance as well.
We want to transpose I = E/R for E and R. The rule is: do whatever you like to the equation and it will always be correct as long as you do the same to each side of the equals sign. For example, if I multiply both sides of the equal sign by R, we get:
I x R = E/R x R
On the left hand side (LHS) we have I x R. On the RHS we have E multiplied by R and divided by R. Can you see that the R’s cancel on the RHS? R/R is 1/1.
I x R = E/1 x 1
There is no need to show the 1′s at all since multiplying or dividing a number by 1 does not change the number, therefore:
I x R = E
Rewriting the above with E on the LHS we get:
E = I x R or just E=IR
When there is no sign between two letters in an equation, like IR above, it is assumed the IR means I x R.
Now transpose the equation for R:
I = E/R
Multiply both sides by 1/E (which is the same as dividing both sides by E):
I x 1/E = E/R x 1/E
On the RHS the E’s cancel out so we can rewrite the equation as:
I x 1/E = 1/R
Or
I/E = 1/R
Turning both sides upside down (remember we can do anything as long as we do the same to both sides):
E/I = R/1
Remove the ’1′, and reverse the sides to get:
R = E/I
So the three equations are:
I = E/R ; E = IR ; R = E/I
I have probably made you bored by now – however it is really important to be able to transpose equations for yourself; for a start, you don’t need to remember so many equations.
So if you know any two of the three in ‘E’, ‘R’ and ‘I’ then you can calculate the missing one.
Finding I when you know E and R:
Finding E when you know I and R:
Finding R when you know I and E:
