Electrical principles - Circuits

Series circuit

Diagram showing two globes connected in series with a battery

Globes connected in series

 

A series circuit has two or more loads connected, one after the other.

The current has only one path it can flow along.

An example of a series circuit is a set of Christmas tree lights. All the globes are placed one after the other.

There is only one path, so the current flow will be the same at any point in the circuit.

 
Diagram showing three resistors connected in series

Circuit diagram showing three resistors connected in series

 

 

The total resistance in a series circuit will be equal to the sum of each individual resistance in the circuit.

The more loads placed in the circuit, the more resistance.

The total resistance for a series circuit is calculated using the following formula:

RT = R1 + R2 + R3

 

 

Kirchoff's voltage law

Diagram showing three resistors connected in series and voltmeter connected in parallel with each resistor to measure voltage drop

Voltmeter across each resistor in a series circuit

Kirchoff's law extends Ohm's law in relation to voltages across resistances in a series circuit. The total supply voltage will be equal to the sum of the voltage drop across each resistor.

Total voltage drop (VT) is calculated using the formula:

VT = V1 + V2 + V3

If both the current flow and each resistance value are known, then Ohm's law can be used to calculate the voltage drop across each resistor.

Eg:

V1 = IR1

 

 

Power dissipation

The power dissipated in a series circuit depends on the supply voltage applied to the circuit and the current flow in the circuit. The current flow depends on the total resistance of the circuit.

From the section on power you know the formula for power dissipation is:

P = VI

The power dissipated in each individual component depends on the resistance of the component. The total power dissipated will be equal to the sum of the power dissipated by each individual resistance. Depending on the values that are known, combinations of the power formula, as well as Ohm's law, can be used to calculate power dissipated (or any other unknown value).

Example

In the above circuit diagram, if the values are:

VT = 20V

R1 = 50Ω

R2 = 20Ω

R3 = 100Ω

The total resistance can be calculated as follows:

RT = R1 + R2 + R3

RT = 50 + 20 + 100

RT = 170Ω

What is the total power dissipated?

You could calculate the current flow and then calculate the power. Instead you could use substitution to get the formula.

In the formula, P = VI substitute the I with VT/RT to give the formula

PT = VT x VT/RT which is the same as

PT = VT2/RT

PT = 202/170

PT = 0.235W or 235mW