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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
Google Images Animation Factory
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