# Resistance in Series and Parallel

## Series Circuits

Series Circuits

### In previous sections the concept of Current flow was discussed. Current is the flow of charge through a circuit and is measured using an Ammeter. The following diagram shows a simple Series circuit with several Ammeters placed throughout :-

In previous sections the concept of Current flow was discussed. Current is the flow of charge through a circuit and is measured using an Ammeter. The following diagram shows a simple Series circuit with several Ammeters placed throughout :-

### In the Above Circuit, there are two Lamps in series with a switch. There are 3 Ammeters in the positions shown.

In the Above Circuit, there are two Lamps in series with a switch. There are 3 Ammeters in the positions shown.

### As the flow of charge cannot change throughout the circuit (it cannot 'leak out'), the reading on all three Ammeters will be the same.

As the flow of charge cannot change throughout the circuit (it cannot 'leak out'), the reading on all three Ammeters will be the same.

### For a Series circuit, the Current will be the same at all points.

For a Series circuit, the Current will be the same at all points.

### A_{1} = A_{2} = A_{3}

A

_{1}= A

_{2}= A

_{3}

## Voltage in Series Circuits

Voltage in Series Circuits

### In previous sections the concept of Voltage was discussed. Voltage is the Energy per unit charge supplied by the battery and is measured using a Voltmeter. The following diagram shows a simple Series circuit with several Voltmeters placed throughout :-

In previous sections the concept of Voltage was discussed. Voltage is the Energy per unit charge supplied by the battery and is measured using a Voltmeter. The following diagram shows a simple Series circuit with several Voltmeters placed throughout :-

### In the Above Circuit, there are two Lamps in Series with a switch. There are three Voltmeters in the positions shown.

In the Above Circuit, there are two Lamps in Series with a switch. There are three Voltmeters in the positions shown.

### The Energy supplied to each Coulomb of Charge must be enough for the Charge to make a full trip round the circuit. This means that each component will use part of this energy.

The Energy supplied to each Coulomb of Charge must be enough for the Charge to make a full trip round the circuit. This means that each component will use part of this energy.

### For a Series circuit, the Voltage at each point will add up to the Supply Voltage.

For a Series circuit, the Voltage at each point will add up to the Supply Voltage.

### V_{s} = V_{1} + V_{2}

V

_{s}= V

_{1}+ V

_{2}

## Resistance in Series Circuits

Resistance in Series Circuits

### In previous sections the concept of Resistance was discussed. Resistance is a measure of how difficult it is for Current to flow. As each Resistor placed in Series acts to reduce the flow of Charge, their effect is to give an overall larger resistance.

In previous sections the concept of Resistance was discussed. Resistance is a measure of how difficult it is for Current to flow. As each Resistor placed in Series acts to reduce the flow of Charge, their effect is to give an overall larger resistance.

### For a Series circuit, the Resistance at each point will add up to the total Resistance.

For a Series circuit, the Resistance at each point will add up to the total Resistance.

### Note - This will continue for as many Resistors as are added, hence the '...'

Note - This will continue for as many Resistors as are added, hence the '...'

## Example 1 -

Example 1 -

### The circuit diagram below shows a simple resistor circuit:-

The circuit diagram below shows a simple resistor circuit:-

### Calculate:-

Calculate:-

### 1. The Resistance of Resistor "r"

1. The Resistance of Resistor "r"

### 2. The Total Resistance in the Circuit

2. The Total Resistance in the Circuit

### Resistance of Resistor "r" :-

Resistance of Resistor "r" :-

### Find V across each 10 Ω Resistor, then use this to find V across Resistor "r". Then calculate the Resistance of "r".

Find V across each 10 Ω Resistor, then use this to find V across Resistor "r". Then calculate the Resistance of "r".

### V_{10 Ω} = I x R = 0.2 x 10 = 2 V

V

_{10 Ω}= I x R = 0.2 x 10 = 2 V

### V_{Total} = 8 V = 2 + V_{r} + 2

V

_{Total}= 8 V = 2 + V

_{r}+ 2

### V_{r} = 8 - 4 = 4 V

V

_{r}= 8 - 4 = 4 V

### R = V / I

R = V / I

### R_{r} = 4 / 0.2

R

_{r}= 4 / 0.2

### R_{r} = 20 Ω

R

_{r}= 20 Ω

### Total Resistance in the Circuit :-

Total Resistance in the Circuit :-

### R_{T} = R_{1} + R_{2} + R_{3}

R

_{T}= R

_{1}+ R

_{2}+ R

_{3}

### R_{T} = 10 + 20 + 10

R

_{T}= 10 + 20 + 10

### R_{T} = 40 Ω

R

_{T}= 40 Ω

## Parallel Circuits

Parallel Circuits

### In previous sections the concept of Current flow was discussed. Current is the flow of charge through a circuit and is measured using an Ammeter. The following diagram shows a simple Parallel circuit with several Ammeters placed throughout :-

In previous sections the concept of Current flow was discussed. Current is the flow of charge through a circuit and is measured using an Ammeter. The following diagram shows a simple Parallel circuit with several Ammeters placed throughout :-

### In the above circuit, there are two lamps in Parallel with a switch. There are 4 Ammeters in the positions shown.

In the above circuit, there are two lamps in Parallel with a switch. There are 4 Ammeters in the positions shown.

### As the total flow of Charge cannot change throughout the circuit (it cannot 'leak out'), the reading on A_{1} and A_{4} will be the same.

As the total flow of Charge cannot change throughout the circuit (it cannot 'leak out'), the reading on A

_{1}and A

_{4}will be the same.

### When the Current enters the Parallel branches, however, There is more than one path for it to follow, meaning that the Current will be shared between the branches.

When the Current enters the Parallel branches, however, There is more than one path for it to follow, meaning that the Current will be shared between the branches.

### For a Parallel circuit, the Current in each branch will be the add up to the supply Current.

For a Parallel circuit, the Current in each branch will be the add up to the supply Current.

### A_{1} = A_{2} + A_{3} = A_{4}

A

_{1}= A

_{2}+ A

_{3}= A

_{4}

## Voltage in Parallel Circuits

Voltage in Parallel Circuits

### In previous sections the concept of Voltage was discussed. Voltage is the Energy per unit Charge supplied by the battery and is measured using a Voltmeter. The following diagram shows a simple Series circuit with several Voltmeters placed throughout :-

In previous sections the concept of Voltage was discussed. Voltage is the Energy per unit Charge supplied by the battery and is measured using a Voltmeter. The following diagram shows a simple Series circuit with several Voltmeters placed throughout :-

### In the above circuit, there are two lamps in Series with a switch. There are three Voltmeters in the positions shown.

In the above circuit, there are two lamps in Series with a switch. There are three Voltmeters in the positions shown.

### As the Voltage is the amount of Energy given to each coulomb of Charge passing through the Circuit and each branch acts as an independent circuit, the Voltage across each branch is the same as the supply Voltage.

As the Voltage is the amount of Energy given to each coulomb of Charge passing through the Circuit and each branch acts as an independent circuit, the Voltage across each branch is the same as the supply Voltage.

### For a Parallel circuit, the Voltage across each branch is equal to the supply Voltage.

For a Parallel circuit, the Voltage across each branch is equal to the supply Voltage.

### V_{s} = V_{1 }= V_{2}

V

_{s}= V

_{1 }= V

_{2}

## Resistance in Parallel Circuits

Resistance in Parallel Circuits

### In previous sections the concept of Resistance was discussed. Resistance is a measure of how difficult it is for Current to flow. It would be expected that adding Resistors (even in Parallel) would cause the total Resistance to increase, however this is not the case. By adding Resistors in Series, the total Resistance is lowered. If the traffic analogy is once again used:-

In previous sections the concept of Resistance was discussed. Resistance is a measure of how difficult it is for Current to flow. It would be expected that adding Resistors (even in Parallel) would cause the total Resistance to increase, however this is not the case. By adding Resistors in Series, the total Resistance is lowered. If the traffic analogy is once again used:-

### As each branch allows current flow, the effect of each Resistor is greatly reduced, giving a larger Current flow.

As each branch allows current flow, the effect of each Resistor is greatly reduced, giving a larger Current flow.

### For a Parallel circuit, the Resistance can be found using the following formula:-

For a Parallel circuit, the Resistance can be found using the following formula:-

### Note - The biggest mistake made in this unit is to calculate the above formula only part way. This formula gives the reciprocal of R_{T}, not R_{T} itself and so must be further manipulated to find R_{T}.

Note - The biggest mistake made in this unit is to calculate the above formula only part way. This formula gives the reciprocal of R

_{T}, not R

_{T}itself and so must be further manipulated to find R

_{T}.

## Example 2 -

Example 2 -

### In the above section of a circuit, there are three resistors in Parallel. What is the total Resistance of this section of the circuit?

In the above section of a circuit, there are three resistors in Parallel. What is the total Resistance of this section of the circuit?

### 1 / R_{t} = 1/R_{1}+ 1/R_{2 }+ 1/R_{3}

1 / R

_{t}= 1/R

_{1}+ 1/R

_{2 }+ 1/R

_{3}

### 1 / R_{t} = (1/3) + (1/6) + (1/9)

1 / R

_{t}= (1/3) + (1/6) + (1/9)

### 1 / R_{t }= 0.61

1 / R

_{t }= 0.61

### R_{t }= 1.6 Ω

R

_{t }= 1.6 Ω