Voltage and Current for Components in Series

If components are in series- voltages add up.
Currents are the same through all components connected in series.

Example: In this circuit the 4V across the resistor and the 2V across the LED add up to the battery voltage: 2V + 4V = 6V.

The current through all parts (battery, resistor and LED) is 20mA.

Voltage and Current for components in Parallel.

Voltages are the same across all components connected in parallel.
Currents add up for components connected in parallel.

Example: In this circuit the battery, resistor and lamp all have 6V across them.

The 30mA current through the resistor and the 60mA current through the lamp add up to the 90mA current through the battery.

Resistors connected in Series.

When resistors are connected in series their combined resistance is equal to the individual resistances added together. For example if resistors R1 and R2 are connected in series their combined resistance, R, is given by:

Combined resistance in series: R = R1 + R2

This can be extended for more resistors: R = R1 + R2 + R3 + R4 +...

Note that the combined resistance in series will always be greater than any of the individual resistances.

Resistors connected in Parallel.

When resistors are connected in parallel their combined resistance is less than any of the individual resistances. There is a special equation for the combined resistance of two resistors R1 and R2:

Combined resistance of two resistors in parallel:

R = R1 × R2

R1 + R2

For more than two resistors connected in parallel a more difficult equation must be used. This adds up the reciprocal ("one over") of each resistance to give the reciprocal of the combined resistance, R:

1 = 1 + 1 + 1 +...

R R1 R2 R3

Combined resistance in parallel will always be less than any of the individual resistances.

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