Cct component - Universiti Sains Malaysia
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Transcript Cct component - Universiti Sains Malaysia
Simple dc circuit
Pg 31-60
HUGHES
Electrical & Electronic
Technology
I
V
Load
A complete connection of a source and a load
Source : voltage source, current source such as battery
Load : resistor, capacitor, inductor
Circuit 3
I
Circuit 1
Circuit 2
V
A network is a combination of several circuits
R1
V1
I
R2
V2
V
V V1 V2
IRt IR1 IR2
therefore
Rt R1 R2
V IRt
V1 IR1
V2 IR2
V1
R2
R3
V IRt
V1 IR1
V3
V
R1
V2
I
V2 IR2
V3 IR3
V V1 V2 V3
IRt IR1 IR2 IR3
therefore
Rt R1 R2 R3
In general for n series of resistor, Rt
Rt R1 R2 R3 ......... Rn
One man decides to connect two lamps of 60W@220V in
series in order to get more light . However he found the lamps
give out very litter light. Why? Can you explain this.
To get full light , we must connect a single lamp to 220V
source , thus we have
V2
P VI
R
P 60
I
0.27 A
V 220
V 2 2202
R
807
P
60
When connect two lamps in series , then
Rt R1 R2 807 807 1614
V
220
I
0.136 A
Rt 1614
Since the current is less then the
lamp cannot give light fully.
I=1.5A
Calculate the voltage across
each of resistors as in figure
and hence calculate the
supply voltage V
V
R1=2
V1
R2=3
V2
R3=8
V3
V1 IR1 1.5 2 3.0 V
V2 IR2 1.5 3 4.5 V
V3 IR3 1.5 8 12.0 V
V V1 V2 V3 3.0 4.5 12.0 19.5 V
I
Calculate the circuit’s current
R1 =40 V
1
V=100V
R2 =50 V2
R3=70 V
3
R R1 R2 R3 40 50 70 160
V 100
I
0.625 A
R 160
V1
R1
R R1 R2
V2
I
V
I
R1 R2
V
R2
V
V1 IR1
R1
R1 R2
V1
R1
V R1 R2
V
V2 IR2
R2
R1 R2
V2
R2
V R1 R2
V2
R2
V R1 R2
10
100
30 R1 100
R1 100 3 100 300
R1 200
R1
V1
Given that R2=100, calculate
R1 in order to obtain an output
voltage 10V across R2
R2
10V
I
V=30V
I
V I1R1 I 2 R2
I1
R1
V
I2
I1
R2
V
R1
V
I2
R2
I I1 I 2
V V
I
R1 R2
I
1
1
V R1 R2
I 1
V R
1 1 1
R R1 R2
but
then
I
I
V
1
R
1
V V V
I
R1 R2 R3
then
In general
I3
I2
R
2
R
3
I
1
1
1
V R1 R2 R3
1 1
1
1
R R1 R2 R3
1 1
1
1
1
.......
R R1 R2 R3
Rn
I
I1
V
R1
I2
1 1 1
R R1 R2
R2
R
R1 R2
R1 R2
R1R2
V IR I
R1 R2
But
Therefore
V I1R1 I 2 R2
R2
I1 I
and
R1 R2
R1
I2 I
R1 R2
I
Calculate I1,I2 and I3
V 110
I1
5.0 A
R1 22
I1
V=110V
V 110
I2
2.5 A
R2 44
I I1 I 2 5.0 2.5 7.5 A
R1
22
I2
R2
44
I
I1
Calculate the effective resistance
and the power supply
V=12V
R1
6.8
I2
R2
4.7
I3
R3
2.2
1 1
1
1
1
1
1
R R1 R2 R3 6.8 4.7 2.2
0.147 0.213 0.455 0.815
1
R
1.23
0.815
Hence
V
12
I
9.76 A
R 1.23
I=8A
Calculate the current in the 2
resistor, given that
I1
(a)R1 =2
(b)R1 =4
V
R1
I2
R2
2
R1
2
I2 I
8
4.0 A
R1 R2
22
I1 = I - I2 = 8 - 4 = 4A
I1 and I2 are equal
R1
4
I2 I
8
5.3 A
R1 R2
42
I1 and I2 are not equal
I1 I I 2 8 5.3 2.7 A
Current Law- At any instant the
algebraic sum of the currents at a
junction in a network is zero
N
I
i
0
i
I1 I 2 I 3 I 4 0
I1
I4
I2
I3
At junction a
I1
R2
a
I4
I3
Determine the relationship
between the currents I1 ,I2, I4
and I5.
R1
R3
I2
I1 I 4 I 3 0
b
I5
I 3 I1 I 4
At junction b I 3 I 5 I 2 0
Hence
Therefore
Then
I3 I 2 I5
I1 I 4 I 2 I 5
or
I1 I 2 I 4 I 5 0
Given that I1=2.5A and I2=-1.5A.
Calculate the current I3.
R2
I1
I3
R3
R1
From Kirchoff’s law
R5
I1 I 2 I 3 0
I2
I 3 I1 I 2 2.5 1.5 1.0 A
R4
a
I1=3A
At junction a
I4
I 2 I1 I 3 3 1 2 A
I6=1A
I 2 I 4 I6 0
I 4 I 6 I 2 1 2 1A
c
I5
I1 I 2 I 3 0
At junction b
I2
I3
Determine the current
I2, I4 and I5.
b
At junction c
I3 I 4 I5 0
I5 I3 I 4 1 1 2 A
Determine the current I1
and I2.
I1
R1=30
Use current divider concept
R2
I3
I1
R2 R3
R2 R3
60 30
I1
I3
1 1.5 A
R2
60
At junction a
I 2 I 3 I1 0
I 2 I1 I 3 1.5 1 0.5 A
a
R2 60
I2
R3=30
I3=1A
Total potential difference across
connected components in a
complete circuit is zero. The
sign of potential difference (p.d)
of the source (or e.m.f) is
always in opposite sign of the
passive components of the
circuit
E V1 V2 V3
or
thus
V1 V2 V3 E 0
n
V
i
i
0
V1
E
V2
V3
E1
E2
V
E3
V E1 E2 E3
Loop C
Determine the Voltage
V1 and V3.
V1
E=12V
Loop A
V2=8V
Loop A
V3
Loop B
E V1 V2
V1 E V2 12 8 4V
Loop B
0 V2 V3 V4
V3 V2 V4 8 2 6V
To check the result
Loop C
E V1 V3 V4
12 4 6 2 12
V4=2V
D
Calculate VAB for the
network shown
R2
R1
Branch A
VAC
R3
15
V
20 7.5V
R1 R3
25 15
20V
25
VAB
A
R3
R4
Branch B
VBC
R4
10
V
20 4.0V
R2 R4
40 10
Applying Kirchoff’s law
0 VAB VBC VCA VAB VBC VAC
VAB VAC VBC 7.5 4.0 3.5V
B
C
Calculate V1 and the e.m.f E2
Kirchoff’s law to left loop
E1 V1 V2
E1=10V
Kirchoff’s law to right loop
E2 V2 V3
E2 V2 V3 6 8 14V
To check again for outside loop
10 14 4 8
V3=8V
V2=6V
V1 E1 V2 10 6 4V
E1 E2 V1 V3
V1
E2