5: Electric Current

5.2 Electric Circuits

Resistor Combinations

Experiment: Resistance in series and parallel circuits.

• Use a voltmeter and ammeter or Ohmmeter to determine the resistance of a range of components.• Then connect them in series or in parallel pairs and investigate the overall resistance.

Resistors in Series

R1 R2

- Current (I) is equal in both

- The supply voltage is shared across the resistors

Vs = V1 + V2

IRe = IR1 + IR2 (Re = total equivalent resistance)

but I cancels out giving…

Re = R1 + R2 for resistors in series

Resistors in Parallel

I = I1 + I2 but... I =

so... V cancels giving...

- Total current (I) is shared between the two resistors

- The voltage across each is equal (V)

I2

R2

R1I

I1

VR

VRe

VR1

VR2

= +

1 Re

1 R1

1 R2

= + for resistors in parallel

E.g. Calculate the equivalent resistance of these resistor combinations:

E.g.2.Put these in increasing order of magnitude

750Ω

1200Ω

1200Ω

120Ω 360Ω

X Y Z

The Potential Divider Circuit

We know that for resistors in series, the supply voltage is shared between the individual resistors.

Demo:

1 kΩ

2 kΩ

V

V1

V2

1. Measure V and the voltages across the two resistors.

2. Predict how the voltages would change if you swapped the 1kΩ resistor for a 4kΩ resistor?

The ratio of the resistances is the same as the ratio of the voltages

Conclusion:

Q. Using V=IR, explain why the bigger resistor will always take a larger voltage.

A circuit like this is known as a potential divider because it divides up the total p.d. supplied by the cell.

The voltage across one of the resistors can then be used as an output supply to an external device or circuit.

E.g.

R1

R2

V

I

Vout

Assuming voltage V is shared across the two resistors…

V = I R V = I (R1 + R2)

I = V R1 + R2

but… Vout = IR2

so… Vout = V R2

R1 + R2

(where R = equivalent resistance)

This is called the potential divider formula

E.g.

a. Determine the total resistance and hence the current in the circuit.

b. Determine the output voltage in the circuit.

c. If a bulb was connected across the output, how would this affect the output voltage?

6Ω 9Ω

V

I

Vout

12V

a. R = 15Ω so… I = 0.8A

b. V = 7.2V

c. A parallel section would be created, thus reducing the total resistance between the output terminals and thus also reducing the output voltage.

Extension: If the bulb has resistance 18Ω, determine the new Vout?

( Demo / Experiment

- LDR, 2.2kΩ, 2 cells, voltmeter )

Sensors and potential dividers

1. Strain gaugeThe diagram below shows part of an F1 car suspension. A strain gauge is stuck on the underside of strut X and wired into the circuit shown.

Explain what a decrease in measured output voltage would indicate.

X

R2

V

I

Vout

Strain gauge

2. Automatic light switch

The electronic switch will turn on the lights (on another circuit) if the voltage rises above a certain fixed value.

i. What happens to the LDR resistance when the light level falls?

ii. So what happens to Vout?

iii. What happens next?

R1

V

I

Vout

Electronic

switch

LDR

The Potentiometer

A potentiometer is a variable potential divider.

R1

R2

V

I

Vout

The slider can be moved to alter the ratio of R1 to R2

A

B

C

Q. At which positions would the slider enable the bulb to i. be brightest?

ii. be off (Vout= 0)?

EMF and Internal Resistance

EMFFor components that put energy into a circuit, the p.d. across them is referred to as the Electro Motive Force (EMF). Therefore…

However the voltage measured across the terminals of the cell (the terminal p.d.) is often less than the EMF.

The EMF of a cell is the amount of work done by the cell per Coulomb of charge passing through the circuit.

Internal Resistance

Demo / Experiment:

V

I 1. Set up the circuit and measure the voltage across the cell.

2. Add one, then two, then three bulbs in parallel. What happens to V?

Observations and Conclusion:

The terminal p.d. decreases as the resistance of the circuit decreases. This indicates that the cell must have resistance itself, taking a gradually larger share of the EMF (this is now like a potential divider circuit).

Internal Resistance

All cells (and other sources of EMF) have an internal resistance, r (effectively in series). This is why cells heat up during use.

EMF

V

Ter

min

al v

olta

ge Lost voltage across r = Ir

Thus…

EMF = Ir + V

but… V = IR

so… EMF = I (r +R)Experiment:

Aim: Determine the internal resistance of a single cell.

rI

R

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V

I

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