True or False?• The electrons in a circuit move in the

same direction as the current.

• The current through a component is directly proportional to the voltage if the resistance of the component stays the same.

• The resistance in a wire is directly to the thickness of the wire.

True or False?

• In a filament lamp the resistance increases with the voltage.

• The electrons lose part of the E.M.F. provided by the battery as they go around the circuit once.

• In a thermistor the resistance is higher when the weather is cooler.

Resistance in Series and Parallel

• Resistance in series circuits

• Resistance in parallel circuits

Resistance in series circuits

Use Ohm’s law to calculate the voltage across the resistors in the next slide.

Write your values in the voltmeters and see if they agree with the actual readings.

.603

1.332

.897

2.2 Ω 1.5 Ω

VoltsVolts

Amps

.601

2.231

2.2 Ω

1.5 Ω

Volts

Amps

What should the voltage across the two resistors be?

Equivalent resistance

0.601 A

2.231 V

The two resistors in the previous series circuit can be thought of as a single resistor. Work out and write the equivalent resistance using Ohm’s law and the values of current and voltage shown.

3.7 Ω

Equivalent resistanceIn a series circuit the total resistance of the components is the sum of the resistance of each component. So, the equivalent resistance R is found as:

R = R1 + R2

3.7 Ω2.2 Ω 1.5 Ω

R1 R2 R

Look at the parallel circuit on the next slide and work out the current in the main circuit and through each resistor in the parallel branches.

Resistance in parallel circuits

1.9911.830

1.716

2.2 Ω

1.5 Ω

Volts

Volts

Amps

What do you think the current in the main circuit should be?

1.144 A

0.832 A

Resistance in parallel circuits

The current in the main circuit is the sum of the currents in the parallel branches:

I = I1 + I2

R1

R2

I

I1

I2

1.9911.830

1.716

2.2 Ω

1.5 Ω

Volts

Volts

Amps

Work out the combined resistance in the main circuit with these values of current and voltage

Using the values of V and I in the previous slide and Ohm’s law to work out the combined resistance, we find:

R1=2.2 Ω

I

I1

I2 R2=1.5 Ω

VI

1.8 V1.99 A

What can you notice about the combined resistance?

Combined resistance

R = = = 0.9 Ω

Combined resistance

The combined resistance R = 0.9 Ω is less than R1 = 2.2 Ω or R2 = 1.5 Ω. You can work out the combined resistance of a parallel circuit using these formulae:

or

21

111

RRR

21

21

RR

RRR

What is the combined resistance when the resistors are the same?

What is the equivalent circuit?

8 A

A

V

12 32

V V

2.5 A

A

V

8 A

12 32

V V

2.5 A

Split the branches in two separate circuits. What is this circuit?This is a series circuit where the current is 2.5 A (the reading inside the branch). What is the voltage across the two resistors?

V = R x I

3080

What is the equivalent circuit?

What is the equivalent circuit?

8 A

A

V

12 32

V V

2.5 A

A

V

8 A

12 32

V V

2.5 A

What is the equivalent resistance and the voltage across?

3080

44

110

Now you can deal with this. What is the voltage, current and resistance?

110

5.520