Equivalent Resistance

Objectives:3.7 Distinguish the equivalent resistance of series and parallel circuits kept at constant temperatures.3.8 Determine the equivalent resistance of a series- parallel circuit kept at constant temperature.3.9 Evaluate the significance of the error in the measurement of electrical resistance.

Circuits:

A circuit is made up of a power supply, connecting wires & various elements that allow current to leave a power source, travel through the elements & return back to the power source.

Common Electric Symbols

Battery/Power Source

Bulb

Common symbols (cont’d)

Switch

Push-button Switch

Resistor

Voltmeter

Ammeter

V

A

Circuits

Power Supply

Resistor

A

Ammeter

v

Voltmeter

Types of Circuits:

There are 2 types of circuits: 1. Series Circuit 2. Parallel Circuit

SERIES

Trick to help identify type of circuit:

Series: Pen follows wire

Parallel: Pen can go in more than one direction

PARALLEL

Series or Parallel?

AA

SERIES

SERIES

PARALLEL

PARALLEL1.

4.3.

2.

Equivalent Resistance - Req

Equivalent Resistance is the TOTAL resistance of a circuit Symbol: Req Units: Ω Ohms

Formula:

Series:

Req = R1 + R2 + R3 + …

Parallel:

...3

1

2

1

1

1

Re

1

RRRq

5

3 10

Type of circuit: Series

Formula: Req = R1 + R2 + R3

Req = 10 + 5 + 3

Req = 18

What is the equivalent resistance (Req) of the circuit below?

30

75

Type of circuit: Series

Formula: Req = R1 + R2

Req = 75 +30

Req = 105

What is the equivalent resistance (Req) of the circuit below?

Type of circuit: Parallel

Formula:

What is the equivalent resistance (Req) of the circuit below?

10 Ω

15 Ω

21

11

Re

1

RRq

1 ÷ 0.1666 = 6Ω

15

1

10

1

Re

1

q

0666.01.0Re

1

q

1666.0Re

1

q

6Req

Type of circuit: Parallel

Formula:

What is the equivalent resistance (Req) of the circuit below?

321

111

Re

1

RRRq

1 ÷ 0.3333 = 3Ω

15

1

5

1

15

1

Re

1

q

0666.02.00666.0Re

1

q

3333.0Re

1

q

3Req

15

5

15

KEY POINTS

321 R1

R1

R1

Req1

Symbols of circuit parts: Voltmeter, Ammeter, Power Supply, Resistor

Two types of circuits (series and parallel)

Formula for Req (equivalent resistance)

Series – Req = R1 + R2 + R3

Parallel -

Activities

Worksheet #10

References

Student Study Guide – Physical Science 416/436 - MEQ

Science Quest – Grenier, Daigle, Rheaume – 1998, Cheneliere

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Alternative Educational Experiences through e-Learning

Relative Error

Whenever your conducting an experiment, the results obtained are only as good as the tools used to do the procedure. Precision, accuracy and reliability are key factors that influence the outcome of any data.

The relative error associated to the results gives a good idea of how good the data obtained is. It can be calculated as;

Err = Absolute error x 100Measured value

Relative Error

The object measures 2.5 cm. The absolute error is 0.25 cm (half of the smallest increment).

Err = 0.25 x 100

2.5 Err = 10 %

2.5 cm + 10 %

1 cm

2 cm

3 cm