8th Edition Hayt Solutions
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NORTHWESTERN UNIVERSITY Department of Electrical and Computer Engineering ECE-221 Fundamentals of Circuits LAB 2: THÉVENIN'S / NORTON'S THEOREM AND KIRCHHOFF'S LAWS
WORKSHEET 1: Theory 1 k
680
680
1 k
1.2 k 1.5 V
1.5 V
1.5 V 1.5 V
1 k
1.2 k
(a)
150
(d)
(c)
(b)
560
Determine the Thévenin’s and Norton equivalents of each of the circuits in Fig. 1. Circuit (a):
Voc =
V
Isc =
A
Req =
A
V
Thevenin
Circuit (b):
Voc =
Norton
V
Isc =
Req =
A
V
A
Thevenin
ECE 221 Lab 2 Worksheet
Norton
Page 1
Circuit (c):
Voc =
Isc =
V
Req =
A
V
A
Thevenin
Circuit (d):
Norton
Voc =
Isc =
V
Req =
A
V
A
Thevenin
Norton
2: Thévenin's and Norton's Theorem 2.1
What defines an ideal voltmeter? An ideal ammeter? Answer 2.1
2.2
To find the internal resistance of the DAU when measuring currents, first set the DAU to measure current. Build the circuit in Fig. 2, and then use the oscilloscope to measure the voltage across the DAU connections. Finally divide this voltage by the measured current. Record V, I, and R = V/I below. Do you think this resistance will cause a significant error for our experiment? Answer 2.2 V=1.5vdc I=1.503 mAdc R=v/i=1000 ohms – will not cause significant error bc internal resistance is very low - Taking the average: voltage across dau = 0.00369 V R=2.455 ohm
ECE 221 Lab 2 Worksheet
Page 2
2.3.
Fill in this table with the measured experiment (Vexp) and theoretical (Vth) voltages and the Iexp and Ith current for each circuit. Vexp Vth % error 1.5012 1.5 0.000799 1.5013 1.5 0.000866 0.90024 0.8929 0.008153 0.37198 0.365 0.018764
Iexp Ith 0.002242 0.002206 0.002758 0.00275 0.002213 0.002206 0.000561 0
%error 0.016319 0.002909 0.003173 #DIV/0!
Assessment and explanation of error:
2.4
What is an ideal voltage source?
Answer 2.4
2.5
Fill in the table and plot (by hand) current vs. voltage. Draw a line extending to the current and voltage intercepts to graphically determine Voc (I = 0) and Isc (V =0). 2 3 4 5 7 9 40 110
1.371 1.408 1.429 1.443 1.459 1.468 1.494 1.498
V
A
Thévenin
Norton
3: Kirchoff's Laws 3.1 DC (V) Vth Fxn Gen Power Supply R1 R2
ECE 221 Lab 2 Worksheet
Vexp
% error #DIV/0! #DIV/0! #DIV/0! #DIV/0!
AC (V) Vth
Vexp
% error #DIV/0! #DIV/0! #DIV/0! #DIV/0!
Page 3
Answer 3.1 DC offset is -0.077 460.88 448.77
3.2 Was the voltage across the power supply after connecting it to the circuit different from that which you set it initially? Can you explain the differences? Answer 3.2
3.3 I(Rl) =
mA
Sum of current at top node =
I(R2) =
mA
I(R3) =
mA
I(pwr spl) =
mA
Answer 3.3
ECE 221 Lab 2 Worksheet
Page 4
mA
WORKSHEET 1: Theory 1 k
680
680
1 k
1.2 k 1.5 V
1.5 V
1.5 V 1.5 V
1 k
1.2 k
(a)
150
(d)
(c)
(b)
560
Determine the Thévenin’s and Norton equivalents of each of the circuits in Fig. 1. Circuit (a):
Voc =
V
Isc =
A
Req =
A
V
Thevenin
Circuit (b):
Voc =
Norton
V
Isc =
Req =
A
V
A
Thevenin
ECE 221 Lab 2 Worksheet
Norton
Page 1
Circuit (c):
Voc =
Isc =
V
Req =
A
V
A
Thevenin
Circuit (d):
Norton
Voc =
Isc =
V
Req =
A
V
A
Thevenin
Norton
2: Thévenin's and Norton's Theorem 2.1
What defines an ideal voltmeter? An ideal ammeter? Answer 2.1
2.2
To find the internal resistance of the DAU when measuring currents, first set the DAU to measure current. Build the circuit in Fig. 2, and then use the oscilloscope to measure the voltage across the DAU connections. Finally divide this voltage by the measured current. Record V, I, and R = V/I below. Do you think this resistance will cause a significant error for our experiment? Answer 2.2 V=1.5vdc I=1.503 mAdc R=v/i=1000 ohms – will not cause significant error bc internal resistance is very low - Taking the average: voltage across dau = 0.00369 V R=2.455 ohm
ECE 221 Lab 2 Worksheet
Page 2
2.3.
Fill in this table with the measured experiment (Vexp) and theoretical (Vth) voltages and the Iexp and Ith current for each circuit. Vexp Vth % error 1.5012 1.5 0.000799 1.5013 1.5 0.000866 0.90024 0.8929 0.008153 0.37198 0.365 0.018764
Iexp Ith 0.002242 0.002206 0.002758 0.00275 0.002213 0.002206 0.000561 0
%error 0.016319 0.002909 0.003173 #DIV/0!
Assessment and explanation of error:
2.4
What is an ideal voltage source?
Answer 2.4
2.5
Fill in the table and plot (by hand) current vs. voltage. Draw a line extending to the current and voltage intercepts to graphically determine Voc (I = 0) and Isc (V =0). 2 3 4 5 7 9 40 110
1.371 1.408 1.429 1.443 1.459 1.468 1.494 1.498
V
A
Thévenin
Norton
3: Kirchoff's Laws 3.1 DC (V) Vth Fxn Gen Power Supply R1 R2
ECE 221 Lab 2 Worksheet
Vexp
% error #DIV/0! #DIV/0! #DIV/0! #DIV/0!
AC (V) Vth
Vexp
% error #DIV/0! #DIV/0! #DIV/0! #DIV/0!
Page 3
Answer 3.1 DC offset is -0.077 460.88 448.77
3.2 Was the voltage across the power supply after connecting it to the circuit different from that which you set it initially? Can you explain the differences? Answer 3.2
3.3 I(Rl) =
mA
Sum of current at top node =
I(R2) =
mA
I(R3) =
mA
I(pwr spl) =
mA
Answer 3.3
ECE 221 Lab 2 Worksheet
Page 4
mA
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