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Potential Division

The 'voltage drop' from a power supply spreads itself out across components in a circuit strand 'fairly'.

The component with the most resistance gets the biggest share of the total potential difference available.

This results in a steady current through the wire strand.

Being able to analyse the distribution of electric potential across a circuit allows you to 'analyse' circuits - it is a very useful art!

Let's work out what the voltage drop would be across the top 900Ω resistor - what would the voltmeter reading be?

Step 1

The three 900Ω resistors in parallel with each other, will each have the same potential difference, as across a parallel arrangement all components have the same potential drop.

But what will this be? It is not easy to see.

We need to replace the three parallel resistors with a single equivalent resistor.

1/RTOTAL = 1/ R1 + 1/R2 + 1/R3

1/RTOTAL= 1/900 + 1/900 + 1/900 = 3/900

so, RTOTAL= 900/3 = 300Ω

 

Step 2

Work out the total resistance:

RTOTAL = R1 + R2 + R3

RTOTAL = 200Ω + 300Ω + 400Ω = 900Ω

Step 3

Work out the potential drop per ohm for the single strand of the circuit.

Total potential drop = 9V

Total resistance = 900 Ω

Each ohm has 9/900 volts across it = 1/100 = 0.01V/Ω

Step 4

Work out the voltage drop across the resistors.

- the 200 Ω resistor has a potential drop of 200 x 0.01 = 2V

- the 300 Ω resistor (the resistor that replaced the parallel arrangement) has a potential drop of 300 x 0.01 = 3V

- the 400 Ω resistor has a potential drop of 400 x 0.01 = 4V

Step 5

Double check that the voltages add up to the source voltage.

It adds up to 9V so it looks okay!

Step 6

Answer the question!

The voltmemter would read 3V

Now try some questions:

Q1. Three resistors are in series 700 Ω, 300 Ω and 200 Ω.

A potentail difference of 6V is applied across the arrangement.

Calculate the potential drop across the 700 Ω resistor.

Q2. Three resistors are in series 900 Ω, 400 Ω and 700 Ω.

A potential difference of 5V is applied across the arrangement.

Calculate the potential drop across the 700 Ω resistor.

Q3. Two sets of resistors are in series with a single 300 Ω resistor.

The first set is composed of two 900 Ω resistors in parallel with each other.

The second set consists of a 400 Ω and 700 Ω resistor in parallel with each other.

A potential difference of 10 V is applied across the arrangement.

What is the voltage drop across the single 300 Ω resistor?

Click here for the solutions