Simple dc circuit Pg 31-60 HUGHES Electrical & Electronic Technology
Dec 22, 2015
Simple dc circuit
Pg 31-60
HUGHES
Electrical & Electronic Technology
A complete connection of a source and a load
Source : voltage source, current source such as battery
Load : resistor, capacitor, inductor
V
I
Load
A network is a combination of several circuits
V
I
Circuit 1
Circuit 3
Circuit 2
V
R 1
R 2
V1
V2
I
11 IRV tIRV
22 IRV
21 RRRt 21 IRIRIRt
21 VVV
therefore
11 IRV tIRV
22 IRV
321 RRRRt 321 IRIRIRIRt
33 IRV
321 VVVV
V
R 3
R 1
R 2
V1
V2
V3
I
therefore
nt RRRRR .........321
In general for n series of resistor, Rt
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.
AR
VI
t
136.01614
220
AV
PI 27.0
220
60
R
VVIP
2
161480780721 RRRt
80760
22022
P
VR
To get full light , we must connect a single lamp to 220V source , thus we have
When connect two lamps in series , then
Since the current is less then the lamp cannot give light fully.
V
R 3=8
R 1=2
R 2=3
I=1.5A
V 1
V 2
V 3
VIRV 0.325.111
VVVVV 5.190.125.40.3321
VIRV 5.435.122
VIRV 0.1285.133
Calculate the voltage across each of resistors as in figure and hence calculate the supply voltage V
V=100V
R 3=70
R 1 =40
R 2 =50
I
V 1
V 2
V 3
Calculate the circuit’s current
160705040321 RRRR
AR
VI 625.0
160
100
V
R 1
R 2
V1
V2
I
221
22 RRR
VIRV
21 RRR
21
11
RR
R
V
V
21 RR
VI
121
11 RRR
VIRV
21
22
RR
R
V
V
V=30V
R 1
R 2
V1
10V
I
Given that R2=100, calculate R1 in order to obtain an output voltage 10V across R2
2001R
100
100
30
10
1
R
30010031001 R
21
22
RR
R
V
V
V
I
R 2R 1
I2I1
11 R
VI
22 R
VI
2211 RIRIV
21 R
V
R
VI
21 III
21
111
RRR
21
11
RRV
I
RV
I 1but then
V
I
R2
R1
I2I 1
R3
I3
321 R
V
R
V
R
VI
321
1111
RRRR
321
111
RRRV
I
then
nRRRRR
1.......
1111
321
In general
V
I
R 2R 1
I2I1
21
21
RR
RRR
21
21 RR
RII
21
111
RRR
21
21
RR
RRIIRV
2211 RIRIV
21
12 RR
RII
But
Therefore and
V=110V
I
R 244
R 122
I2I1
Calculate I1,I2 and I3
AR
VI 5.2
44
110
22
AR
VI 0.5
22
110
11
AIII 5.75.20.521
V=12V
I
R 32.2
R 16.8
I2I1
R 24.7
I3
815.0455.0213.0147.0
2.2
1
7.4
1
8.6
11111
321
RRRR
23.1815.0
1R A
R
VI 76.9
23.1
12
Calculate the effective resistance and the power supply
Hence
V
I=8A
R 22
R 1
I2I1
ARR
RII 0.4
22
28
21
12
ARR
RII 3.5
24
48
21
12
I1 = I - I2 = 8 - 4 = 4A
AIII 7.23.5821
I1 and I2 are not equal
Calculate the current in the 2 resistor, given that
(a)R1 =2 (b)R1 =4
I1 and I2 are equal
Current Law- At any instant the algebraic sum of the currents at a junction in a network is zero
I1
I4I3
I2
04321 IIII
0N
iiI
R 1 R 2
R 3
I1 I4
I2
I3I5
a
b
Determine the relationship between the currents I1 ,I2, I4 and I5.
413 III
0341 IIIAt junction a
05421 IIII
523 III
Hence
5241 IIII
0253 IIIAt junction b
Therefore
Then or
R 2
R 5
R 1R 4R 3
I3I1
I20321 III
AIII 0.15.15.2213
From Kirchoff’s law
Given that I1=2.5A and I2=-1.5A. Calculate the current I3.
I6=1A
I5
I4I3I1=3A I2
a
b
c
0321 III
AIII 121264
At junction a
Determine the current I2, I4 and I5.
At junction b
AIII 213312
0543 III
At junction c0642 III
AIII 211435
R 1=30
I1
I3=1AI2
R 3=30 R 2 60 132
23 I
RR
RI
AIII 5.015.1312
Use current divider concept
Determine the current I1
and I2.
AIR
RRI 5.11
60
30603
2
321
At junction a
0132 III
a
E
V 3
V 1
V 2
0n
iiV
321 VVVE
0321 EVVV
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
or
thus
E 2
E 1
V
E 3
321 EEEV
21 VVE
VVVV 628423
Loop A
Determine the Voltage V1 and V3.
Loop B
VVEV 481221
431 VVVE
Loop C
4320 VVV
1226412
E=12V
V 3V 1 V 2=8V
V 4=2VLoop BLoop A
Loop C
To check the result
20V A
V AB
R 1
25
R 4R 3
R 2
C
B
D
VVRR
RVAC 5.720
1525
15
31
3
ACBCABCABCAB VVVVVV 0
Branch A
Branch B
VVVV BCACAB 5.30.45.7
Applying Kirchoff’s law
VVRR
RVBC 0.420
1040
10
42
4
Calculate VAB for the network shown
E 1=10V
V 1
V 3=8V
V 2=6V
E 2211 VVE
3121 VVEE
Kirchoff’s law to left loop
841410
To check again for outside loop
322 VVE
Calculate V1 and the e.m.f E2
VVEV 4610211
VVVE 1486322
Kirchoff’s law to right loop