Series and Parallel Circuits

Series circuits

A series circuit is a circuit in which resistors are arranged in a chain, so the current has only one path to take. The current is the same through each resistor. The total resistance of the circuit is found by simply adding up the resistance values of the individual resistors:
equivalent resistance of resistors in series : R = R1 + R2 + R3 + ...

A series circuit is shown in the diagram above. The current flows through each resistor in turn. If the values of the three resistors are:
R1=8 ohms, R2=8 ohms and R3=4 ohms
The total resistance is R1 + R2 + R3= 20 ohms

With a 10 V battery, by V = I R the total current in the circuit is:
I = V / R = 10 / 20 = 0.5 A. The current through each resistor would be 0.5 A.

Parallel circuits

A parallel circuit is a circuit in which the resistors are arranged with their heads connected together, and their tails connected together. The current in a parallel circuit breaks up, with some flowing along each parallel branch and re-combining when the branches meet again. The voltage across each resistor in parallel is the same.
The total resistance of a set of resistors in parallel is found by adding up the reciprocals of the resistance values, and then taking the reciprocal of the total:
equivalent resistance of resistors in parallel: 1 / R = 1 / R1 + 1 / R2 + 1 / R3 +...
A parallel circuit is shown in the diagram above. In this case the current supplied by the battery splits up, and the amount going through each resistor depends on the resistance. If the values of the three resistors are:
R1=8 ohms, R2=8 ohms and R3=4 ohms
The total resistance is found by 1/R = 1/8+1/8+1/4 = 1/2
that gives R = 2 ohms

With a 10 V battery, by V = I R the total current in the circuit is: I = V / R = 10 / 2 = 5 A.
The individual currents can also be found using I = V / R. The voltage across each resistor is 10 V, so:
I1 = 10 / 8 = 1.25 A
I2 = 10 / 8 = 1.25 A
I3=10 / 4 = 2.5 A
Note that the currents add together to 5A, the total current.