Download Electricity Tutorial Sheet 2 2011

Foundation Engineering Science Electric Circuits: Tutorial Sheet 2
2011/12
Chapter 2 Electric Circuits
Tutorial 2: Solutions
Question 2.1:
240 V is supplied to the DC motor with the resistance of 48 Ω. Find the electric current flowing
in the motor.
Answer:
I
V 240

 5A
R 48
Question 2.2:
The internal voltage of a cell is 3 V and its internal resistance is 2 Ω. If the cell is used as a
power source to an external resistance 2.5 Ω, what is the total resistance in the circuit? And
what is the current flowing through the whole circuit?
3.0V
+
-
2Ω
Cell
2.5 Ω
I
Figure for Question 2.2
Answer:
The total resistance RT is
RT  R1  R2  2  2.5  4.5
The current I is
I
V
3
2

  0.667 A
RT 4.5 3
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Foundation Engineering Science Electric Circuits: Tutorial Sheet 2
Question 2.3:
The following resistor network is set up.
Calculate the total resistance of the network.
Answer:
1
1
1
1
1 1 1



    0.083  0.056  0.167  0.306 1
RT R1 R2 R3 12 18 6
RT 
1
 3.27
0.306
Question 2.4
Find the total resistance of the network as shown in Figure for Question 2-4.
12 Ω
32 Ω
24 Ω
Figure for Question 2-4
Step 1: subtotal resistance Rp of 12 Ω and 24 Ω
1
1
1 2 1 3 1
 



R p 12 24
24
24 8
So R p  8 Ω.
Step 2: total resistance RT
RT  32  8  40 Ω.
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Foundation Engineering Science Electric Circuits: Tutorial Sheet 2
2011/12
Question 2.5
Find the total resistance of the network as shown in Figure for Question 2.5.
36 Ω
12 Ω
24 Ω
Figure for Question 2.5
Step 1: subtotal resistance RS of 12 Ω and 36 Ω
RS  12  36  48 Ω.
Step 2: total resistance RT
1
1
1 2 1 3
1





Ω
RT 24 48
48
48 16
So RT  16 Ω.
Question 2.6:
In the specification table of a cell, you can find that the cell can supply the electric power of 30
W and its voltage is specified as 10 V. If the cell is to power a DC motor, what is the minimum
resistance the motor should have?
Answer:
The current is permitted in the cell is
I
P 30

 3A
V 10
If the cell is powered to the motor without any loss and the voltage across the motor is 10 V,
then the current travelling in the DC motor is
I  3A
According to Ohm’s law, the resistance of the motor should be
R
V 10

 3.3 Ω.
I
3
3.3 Ω is the minimum resistance. If you elect to use a smaller resistance, e.g., 2 Ω, then
I
V 10
  5 A.
R 2
It is higher than the permitted current 3A (or max power of the cell) and hence the cell may
overheat and become damaged or cause a fire.
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Foundation Engineering Science Electric Circuits: Tutorial Sheet 2
2011/12
Question 2.7:
Two resistors R1 and R2 are connected in parallel in a circuit as shown in Figure for Question
2.7. Show that the formula for the relationship between the total resistance RT and the
individual R1 and R2 is given by
RT 
R1 R2
R1  R2
Answer:
VT
-
+
IT
I1
V1
R1
I2
V2
R2
2
Figure for Question 2.7
The currents in the circuit obey Kirchhoff’s current law and so we have
I T  I1  I 2
VT V1 V2


RT R1 R2
The voltages in the circuit obey Kirchhoff’s voltage law and so we have
VT  V1  V2
1
1
1 R2  R1



RT R1 R2
R1 R2
RT 
R1 R2
R1  R2
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Foundation Engineering Science Electric Circuits: Tutorial Sheet 2
Question 2.8
Find the total resistance of the network as shown in Figure for Question 2-8.
14 Ω
16 Ω
12 Ω
8Ω
Figure for Question 2.8
Step 1: subtotal resistance RS1 of 14 Ω and 16 Ω and RS2 of 12 Ω and 8 Ω
RS1  14  16  30
RS 2  12  8  20
Step 2: total resistance RT
1
1
1
2
3 23 5
1






 
RT 30 20 60 60
60
60 12
So RT 12
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2011/12