Download Current and Voltage

Combining Resistors
Objective:
To work out the total equivalent resistance of a
multiple of resistors in a circuit.
Starter quiz
9V
V1
What would the reading on V3 be?
a. 3V
M
b. 5V
c. 7V
d. 9V
N
V2
2V
V
P
V3
?V
Which meter is in the wrong place?
a.
A1, A2 & A3
b.
A2 & A3
c.
V1 & V2
d.
V1
A1
A2
V3
V2
A3
V3
Which meter is in the wrong place?
a.
A1, A2 & A3
b.
A2 & A3
c.
V1 & V2
d.
V1
A1
A2
V3
V2
A3
V3
6A
?A
A
4Ω
Circuit W
A
2Ω
Circuit Z
What is a possible reading for the ammeter in circuit Z?
a. 0A
b. 3A
c. 6A
d. 12A
6A
A
4Ω
Circuit W
What is the voltage across the 4Ω resistor?
a. 24 V
b. 10V
c. 6V
d. 1.5 V
12V
6A
A
?Ω
What is the value of the resistance in the circuit?
a. 0Ω
b. 2Ω
c. 6Ω
d. 12Ω
??? V
2A
A
8Ω
What is the voltage supplied by the cell in this circuit?
a. 4V
b. 16V
c. 32V
d. 64V
6A
12V
4Ω
4Ω
The current from the battery is 6A, how much is
the current through the 4Ω resistor ?
6A
12V
4Ω
4Ω
The current from the battery is 6A, how much is
the current through the 4Ω resistor ?
3A
12V
A 3Ω resistor and a 6Ω
connected in parallel.
Which resistor passes the
most current ?
3Ω
6Ω
12V
A 3Ω resistor and a 6Ω
connected in parallel.
Which resistor passes the
most current ?
3Ω
6Ω
The 3Ω resistor
Last q
Which of the following current-voltage graphs is of light bulb ?
A
Current (A)
C
Current (A)
Current (A)
B
Voltage (V)
Voltage (V)
Voltage (V)
Last q
Which of the following current-voltage graphs is of light bulb ?
A
Current (A)
C
Current (A)
Current (A)
B
Voltage (V)
Voltage (V)
Voltage (V)
Combining Resistors
Objective:
To work out the total equivalent resistance of a
multiple of resistors in a circuit.
Combining Resistors
Resistors in series:
The total resistance RT of any number of resistors R1 , R2 , R3, ….
connected in series is given by the formula:
RT = R1 + R2+ R3 + …….
Example: A 6Ω resistor in series with a 4Ω
resistor are equivalent to a 10Ω resistor.
Resistors in parallel:
R1
R2
6Ω
4Ω
The total resistance RT of any number of resistors R1 , R2 , R3, ….
connected in parallel is given by the formula:
1
1
1
1
=
+
+
+ …..
RT
R1
R2
R3
Example: A 6Ω resistor in parallel with a 4Ω
resistor are equivalent to :
1
1
1
1
1
=
+
+
0.416
=
=
RT
R1
6
R2
4
RT = 1 / 0.416 = 2.4Ω
R1
6Ω
R2
4Ω
Next: proof
Example
20Ω
RT
30Ω
Find the equivalent resistor that can replace two resistors in
parallel: R1 = 20Ω, R2 = 30Ω
1
1
1
=
+
RT
R1
R2
1
1
1
=
+
RT
20
30
1
= 0.08333
RT
RT = 12Ω
For the mathematically challenged beings: if the
combination had only two resistors in parallel, then:
RT = R1 R2 / (R1+R2) or ‘product over sum’.
This can save the faint-hearted from reciprocals!
Next: investigation
Investigating resistors in series and parallel
Investigating resistors in series and parallel (20 min)
Use the Ohmmeter to measure the resistance of resistor X, Y, Z
Use resistors X, Y and Z to create the different combinations shown
below.
X = ………… Ω
Y = ………… Ω
Combination
Predicted equivalent
resistance / Ω
X
Y
Y
X
Z
X
Z
Y
Z
X
Y
Z
Z = ………… Ω
Measured equivalent resistance / Ω
Investigating resistors in series and parallel
Use the Ohmmeter to measure the resistance of resistor X, Y, Z
Use resistors X, Y and Z to create the different combinations shown
below.
X = ………… Ω
Y = ………… Ω
Combination
Predicted equivalent
resistance / Ω
X
Measured equivalent resistance / Ω
15 Ω
Y
Y
X
Z = ………… Ω
Z
35 Ω
4Ω
X
Z
Y
6.7 Ω
Z
X
Y
Z
8.6 Ω
Next: plenary
What is RT ?
50Ω
40Ω
50Ω
a. 40Ω
b. 90 Ω
c. 65 Ω
d. 140 Ω
What is RT ?
50Ω
100Ω
50Ω
200Ω
40Ω
a. 40Ω
b. 132 Ω
c. 25 Ω
d. 67 Ω
What is RT ?
20Ω
10Ω
40Ω
25Ω
15Ω
a. 50 Ω
b. 132 Ω
c. 25 Ω
d. 63 Ω
What is RT ?
100Ω
100Ω
200Ω
a. 450 Ω
b. 532 Ω
c. 500 Ω
d. 600 Ω
100Ω
100Ω
What is RT ?
50Ω
40Ω
70Ω
30Ω
a. 110 Ω
b. 50 Ω
c. 45 Ω
d. 55 Ω
What is RT ?
Last q
20Ω
10Ω
10Ω
10Ω
a. 50 Ω
b. 20 Ω
c. 5 Ω
d. 1 Ω
Combining Resistors
Objective:
To work out the total equivalent resistance of a
multiple of resistors in a circuit.