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# Series and parallel circuits

Circuits
Left: Series  | Right: Parallel
Arrows indicate direction of current flow.
The red bars represent the voltage.

In electrical circuits series and parallel are two basic ways of wiring components. As a demonstration, consider a very simple circuit consisting of two lightbulbs and one 9V battery. If a wire joins the battery to one bulb, to the next bulb, then back to the battery, in one continuous loop, the bulbs are said to be in series. If, on the other hand, each bulb is wired separately to the battery in two loops, the bulbs are said to be in parallel.

The measurable quantities used here are R, resistance, measured in ohms (Ω), I, current, measured in amperes (coulomb per second), and V, voltage (joule per columb), measured in volts.

## Series Circuits

The same current has to pass through all the components in the loop. An ammeter placed anywhere in the circuit would measure the same amount.
• To find the total resistance of all the components, add together the individual resistance of each component;

Rtotal = R1 + R2

for two components in series, having resistance R1 and R2 respectively. For more than two components, add in their respective resistances.

I = V/Rtotal

• To find the voltage across any particular component with resistance Ri , use Ohm's law again.
V=IRi
Where I is the current, as calculated above.

Note, that the components divide the voltage according to their resistances, so V1/V2 = R1/R2

Inductors follow the same law, in that the total inductance of inductors in series is equal to the sum of their individual inductances:

Capacitors follow a different law. The total capacitance of capacitors in series is equal to the reciprocal of the sum of the reciprocals of their individual capacitances:

## Parallel Circuits

The
voltage is the same across all the components in the loop.

• To find the total current, I, use Ohm's law in each loop then sum.(See Kirchhoff's Laws for an explanation of why this works)
Itotal = V/(R1 + R2 + ...)

• To find the total resistance of all the components, add together the individual reciprocal of each resistance of each component, and take the reciprocal;

1 / Rtotal = 1 / R1 + 1 / R2

for two components in parallel, having resistance R1 and R2 respectively. For more than two components, add in their respective reciprocals of resistances, and take the reciprocal.

The above rule can be calculated by using Ohm's law for the whole circuit
Rtotal =V/Itotal
and substituting for Itotal

• To find the current in any particular component with resistance Ri , use Ohm's law again.
Ii = V/Ri

Note, that the components divide the current according to their reciprocal resistances, so I1/I2 = R2/R1

Inductors follow the same law, in that the total inductance of inductors in parallel is equal to the reciprocal of the sum of the reciprocals of their individual inductances:

Capacitors follow a different law. The total capacitance of capacitors in parallel is equal to the sum of their individual capacitances: