Series and Parallel Circuits

Parallel circuits have more than one path for the current to flow along, they are set up in "branches".  Each branch receives the supply voltage and the current is shared.  In a series circuit if one component fails then the circuit is broken and current can't flow.  In a parallel circuit if one component fails the others can still operate as they are in a different branch.


Resistors can only come in certain values and so it may be necessary to connect them in series or parallel to create a different total resistance.

Resistors in parallel use the equation:
 1       1       1     1
Rt = R1 + R2 + R3 . . .  (this is absolutely not the same as Rt = R1 + R2 + R3!)

This is known as the reciprocal.  You don't need to understand the maths, but it helps if you do.  The reciprocal is the inverse of a number.  You may find this website useful.


Consider this circuit:

We need to find the total or equivalent resistance of the pair of resistors.

Because there are only two resistors it is possible to use the special equation: 

WARNING!  If you plug these numbers straight into your calculator, it will follow BODMAS and so do everything else and then add R2 at the end.  Therefore you must either do the two sums separately and then divide, or use the brackets function on your calculator.


 Current in a parallel circuit is shared between the branches.  Kirchoff's current law states:

The current entering a node (join) equals the current exiting a node.  We use this to show that when the current splits at the node the total current = the sum of the currents in all the branches of a parallel circuit.

So we can find out both the total circuit current and the current in each of the branches:

       V 
IT = RT
         12
     = 825
     = 14.5mA

        V                                  V
I1 = R1                                      I2 = R2
         12                                 12
     = 1100                         = 3300
     = 10.9mA                    = 3.63mA


Check:  IT = I1 + I2
                  = 10.9 x 10-3 + 3.63 x 10-3
                       = 14.5mA                               So our calculations are correct!