DC Circuit Lab Report
fahad17
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EXPERIMENT THREE DC CIRCUITS
EQUIPMENT NEEDED:
1) DC Power Supply 2) DMM 3) Resistors 4) ELVIS
THEORY Kirchhoff's Laws: Kirchhoff's Voltage Law: The algebraic sum of the voltages around any closed path is zero.
N
i iv
1
1.30
Kirchhoff's Current Law: The algebraic sum of the currents at any node is zero.
N
i ii
1
2.30
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Series Circuits: In a series circuit the current is the same through all the elements.
Figure 3. 1
The total series resistance RS is given by
3.3121 NNS RRRRR
and
4.3SS IRV
The Kirchhoff's voltage law indicates that:
5.3121 NNS VVVVV
V
R
+ V1 
R
+ V2 
R
 VN +  VN1 +
RN
I
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The voltages across resistors can be obtained by multiplying the current by the corresponding resistors.
6.3
1 1
2 2
1 1
11
22
11
S S
N N
S S
N N
S S
S S
S
S
NN
NN
V R RV
V R RV
V R RV
V R RV
R VI
IRV
IRV
IRV
IRV
The last expressions of equation 3.6 are known as voltage division.
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Parallel Circuits: In a parallel circuit the voltage is the same across all the elements.
Figure 3. 2
The total parallel resistance, Rp is given by
7.3 11111
121 NNP RRRRR
and
8.3PPP RIV
Kirchhoff's current law states:
9.3121 NNP IIIII
I RI RI RNIN RI PV P
+

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The current through the branch resistors can be obtained by dividing the terminal voltage PV
by the corresponding branch resistance, R. therefore:
10.3
1 1
2 2
1 1
1 1
2 2
1 1
P N
P N
P N
P N
P P
P P
PPP
N
P N
N
P N
P
P
I R RI
I R RI
I R RI
I R RI
RIV
R VI
R VI
R VI
R VI
The last expressions of equation 3.10 are known as current division.
The reciprocal of resistance is known as conductance. It is expressed in the following equa tions:
11.31 R
G
and
12.3 1
P P R G
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This expression can be used to simplify equations 3.12 as shown below.
13.3
1 1
2 2
1 1
11
22
11
P P
N N
P P
N N
P P
P P
P
P P
PNN
PNN
P
P
I G GI
I G GI
I G GI
I G GI
G IV
VGI
VGI
VGI
VGI
where
14.31111
121 NN P RRRR G
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If only two resistors make up the network, as shown next
Figure 3.3
then the current in branches 1 and 2 can be calculated as follows:
18.31
17.311
16.31
15.3
21
2 1
21
21
1 1
21
21
21
1 1
1 1
PP
PP
P P
I RR
RII RR RR
R I
RR RRG
RR G
and
R G
I G GI
In a similar fashion it can be shown that
19.3 21
1 2 PIRR
RI
(Note how the current in one branch depends on the resistance in the opposite branch)
R1 I1
R2 I2
IP
28
But, if the network consists of more than two resistors  say four
Figure 3.4 Then the calculation or branch currents using individual resistance becomes complex as demonstrated next, e.g.,
21.3111111
20.3
4321
321421431432
4321
3 3
RRRR RRRRRRRRRRRR
RRRRRR
I R RI
PP
P P
so that
22.31
321421431432
4321
3 3 PIRRRRRRRRRRRR
RRRR R
I
and
23.3 321421431432
421 3 PIRRRRRRRRRRRR
RRRI
R3
I3
R4
I4
IP R1
I1
R2
I2
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By using conductances, the above is simplified to
24.31111
1
4321
3 3 PI
RRRR
RI
and is easily accomplished with a hand calculator. As the above demonstrates, when using current division, always use conductances and avoid using resistances in the calculation for all parallel networks with more than two resistors.
Series  Parallel Circuits
The analysis of series parallel circuits is based on what has already been discussed. The solution of a seriesparallel circuit with one single source usually requires the computation of total resistance, application of Ohm's law, Kirchhoff's voltage law, Kirchhoff's current law, vol tage and current divider rules. Preliminary Calculations:
Be sure to show all necessary calculations. l. The resistors used in this lab all have 5% tolerances. This is denoted by the gold band. Calculate the minimum and maximum values for resistances with nominal values of 1kΩ and 2.7kΩ. Enter the values in Table 3.1. 2. Assume that the two resistors of problem 1 are used in the circuit of Figure 3.5. Calculate v1, v2, and when R1 and R2 take on their minimum and maximum values and enter in Table
3.2.
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Figure 3.5
3. From your calculations in 2, record the maximum and the minimum possible values of , v1, and v2 that you should see in the circuit in Table 3.3. Also, calculate and record the value of these variables when R1 and R2 are at the nominal values. What is the maximum % error in
each of the variables possible due to the resistor tolerances? 4. For the circuit of Figure 3.6 calculate the resistance between nodes: a. a and b (Rab) b. a and c (Rac) c. c and d (Rcd)
Enter your results in Table 3.4 Hint: Part c cannot immediately be reduced using series and parallel combinations.
R2
2.7kΩ
R1 1kΩ
10V
I + V1 
+ V2 
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Figure 3.6
5. Use voltage division to calculate V1 and V2 for the circuit in Figure 3.7. Enter your re
sults in Table 3.5.
Figure 3.7
3.3kΩ 2.7kΩ
1kΩ
15V
4.7kΩ
+ V1 
+ V2 
3.3kΩ
1kΩ 1kΩ
2.7kΩ
2.7kΩ
d
a b
c
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6. For the circuit in Figure 3.8, if R = 1k ohm, calculate Use current division to calculate
R. Enter your results in Table 3.6. Repeat for R = 2.7k and 3.3k ohms.
Figure 3.8
7. For the circuit in Figure 3.9, calculate each of the variables listed in Table 3.7.
Figure 3.9
Procedure
3.3kΩ 2.7kΩ
1kΩ
10V
4.7kΩ
1kΩ
I1
I3
I2 I4
I5
+ V1  + V2 
 V5 +
+ V3 
+ V4 
R 1kΩ
100kΩ
15V
I IR
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l. Place a wire between the two measuring terminals of the ohmmeter and adjust the mea surement reading to zero ohms. Obtain a 1kΩ and 2.7kΩ resistor and measure their values with the ohmmeter. What is the % error as compared to their nominal values? Enter your re sults in Table 3.1. 2. Construct the circuit in Figure 3.5. Measure V1 and V2 using the DMM only. Calculate
from your measurements. What is the % error as compared to their nominal values? Enter your results in Table 3.3. 3. Construct the circuit of Figure 3.6. Use an ohmmeter to measure the resistances listed in Table 3.4. Calculate the % error. 4. Construct the circuit of Figure 3.7. Measure V1 and V2 using the DMM only. Calculate
the % error. Enter your results in Table 3.5. 5. Construct the circuit of Figure 3.8. Find and R for R = 1kΩ, 2.7 kΩ, and 3.3 kΩ by mea
suring the appropriate voltages using the DMM only and applying Ohm's Law. Enter your re sults in Table 3.6. Note that is approximately constant. Why? 6. Construct the circuit of Figure 3.9. Using the DMM, measure each of the variables listed in Table 3.7, and calculate the % error for each. Verify that KVL holds for each of the 3 loops in the circuit. Verify that KCL holds at each node. What can be said about 2+ 3 and 1?
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Table 3.1
Rnominal Rmin Rmax Rmeas % error 1kΩ
2.7kΩ Table 3.2
R1,min R2, min
R1, max R2, min
R1, min R2, max
R1, max R2,max
I V1 V2
Table 3.3
max min nom max % error
meas % error
V1 V2 I
Table 3.4
Resistance Calculated Measured % error Rab Rac Rcd
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Table 3.5 Calculated Measured % error
V1 V2
Table 3.6
R I, calc IR, calc I, meas IR, meas 1kΩ
2.7kΩ 3.3kΩ
Table 3.7 PARAMETER CALCULATED MEASURED % ERR
V1 V2 V3 V4 V5 I1 I2 I3 I4 I5