Download HW4

Chris Schmitz - ECE 110 Spring 2015
HW4
1
Contents
L6P15.problem .
L6P05.problem .
L6P06.problem .
L6P14.problem .
E2P01.problem .
E2P03.problem .
L5P12.problem .
E2P04.problem .
L6P16.problem .
L6P17.problem .
L6P18.problem .
L6P19.problem .
L6P20.problem .
L6P21.problem .
L7P11.problem .
L7P04.problem .
L7P05.problem .
L7P12.problem .
L7P13.problem .
L7P14.problem .
L7P15.problem .
L7P20.problem .
L8P01.problem .
L8P03.problem .
L8P06.problem .
L8P10.problem .
L8P02b.problem
L9P10.problem .
L9P11.problem .
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2
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23
Chris Schmitz - ECE 110 Spring 2015
HW4
2
Due date: Fri Feb 20 03:00:00 pm 2015 (CST)
R1 = 5 ohms R2 = 9 ohms R3 = 8 ohms
What is the equivalent resistance of these three resistors when looking into the terminals from the left?
·R2 ·R3
A. RR1 1+R
= 16.3636363636364 Ohms
2 +R3
1 ·R2 ·R3
B. R1 ·R2 R
+R2 ·R3 +R1 ·R3 = 2.29299363057325 Ohms
C. R1 + R2 + R3 = 22 Ohms
D. min(R1 , R2 , R3 ) = 5 Ohms
Tries 0/2
R1 = 7 ohms R2 = 7 ohms R3 = 10 ohms
Can series/parallel reduction methods be used to find the equivalent
resistance of this circuit without any other types of transformations?
A. Yes
B. No
If so, Rab = (if not, write 0)
Tries 0/6
ohms
Chris Schmitz - ECE 110 Spring 2015
HW4
3
R1 = 9 ohms R2 = 7 ohms R3 = 9 ohms R4 = 9 ohms R5 = 7 ohms R6 = 10 ohms
Imagine using an ohmmeter to measure the resistance between the nodes with labels a and b. For the circuit above,
answer the following questions to see if we can predict this resistance by using our basic tools to combine resistors in
series and resistors in parallel.
Element R1 and Element R5 are in series:
4.
A
Yes
B
No
Element R1 and Element R2 are in parallel:
5.
A
Yes
B
No
Tries 0/6
Element R2 and Element R4 are in parallel:
6.
A
Yes
B
No
Element R3 and Element R4 are in series:
7.
A
Yes
B
No
Element R5 and Element R6 are in series:
8.
A
Yes
B
No
Chris Schmitz - ECE 110 Spring 2015
HW4
4
Can series/parallel reduction methods be used to find the equivalent
resistance of this circuit without any other transformations?
A. Yes
B. No
If so, Rab =
Ω (enter 0 if it cannot be done)
Tries 0/6
R1 = 6 ohms R2 = 10 ohms R3 = 7 ohms R4 = 4 ohms R5 = 5 ohms
Can series/parallel reduction methods be used to find the equivalent
resistance of this circuit, between terminals a and b, without any other transformations?
A. Yes
B. No
Tries 0/6
Chris Schmitz - ECE 110 Spring 2015
HW4
5
The circuit below contains two ideal instruments (ammeter and voltmeter):
VS = -1 V R = 4 ohm
a) Determine the voltage V1 across the ideal ammeter (in volts), and then use KVL to determine Vm across the ideal
voltmeter (in volts).
V1 =
V
Vm =
V
Tries 0/6
b) Use Ohm’s Law to determine the current I thru the resistor R (in amps).
A
I=
Tries 0/6
The circuit below contains an ideal ammeter:
VS = 24 V R1 = 1 ohm R2 = 2 ohm
Chris Schmitz - ECE 110 Spring 2015
HW4
6
a) Determine the voltage V2 across the ideal ammeter (in volts), and then use KVL to determine V1 across the resistor
R1 (in volts).
V
V2 =
V1 =
V
Tries 0/6
b) Use Ohm’s Law to determine the current I1, I2, and then KCL to determine the current Im (in amps).
A
I1 =
I2 =
A
Im =
A
Tries 0/6
What is the total number of nodes in the circuit?
Tries 0/6
(1) Given that
V2 = 18 V, V3 = -24 V, and V6 = 39 V, use KVL to find V1, V4, and V5.
v1=
V,
V,
v4=
V
v5=
Tries 0/6
(2) Given that
I2 = 39 A, I3 = 1 A, and I6 = 43 A, use KCL to find I1, I4, and I5.
i1=
A,
i4=
A,
i5=
A
Chris Schmitz - ECE 110 Spring 2015
HW4
VS = 8 V Rbias = 40 kΩ
Determine the voltage VA when the flex sensor takes on its minimum value of Rflex=50 kΩ.
VA =
V
Determine the voltage VA when the flex sensor takes on its maximum value of Rflex=100 kΩ.
V
VA =
Tries 0/6
7
Chris Schmitz - ECE 110 Spring 2015
HW4
Voltage Divider Circuit
Find the voltage V3.
Here are the circuit values:
Vs = 6 V
R1 = 1 kΩ
R2 = 6 kΩ
R3 = 3 kΩ
V3 =
Tries 0/6
V
8
Chris Schmitz - ECE 110 Spring 2015
HW4
Voltage Divider Resistor Network
Find the voltage V4.
Here are the circuit values:
Vs1 = 47 V
R1 = 622 Ω
R2 = 200 Ω
R3 = 300 Ω
V4 =
Tries 0/6
V
9
Chris Schmitz - ECE 110 Spring 2015
HW4
Two Voltage Source Circuit
Find the voltage across the nodes x and y.
Here are the circuit values:
Vs1 = 26 V
Vs2 = 40 V
R1 = 8 kΩ
R2 = 5 kΩ
R3 = 6 kΩ
R4 = 4 kΩ
First, compute Vzy (use KVL)
Vzy = V5 =
V
Tries 0/6
Then, compute Vxy (use VDR)
Vxy = V6 =
Tries 0/6
V
10
Chris Schmitz - ECE 110 Spring 2015
HW4
11
Current Divider
In the circuit above, we know that
Is = 0.5 A R2 = 100 Ω
Find the resistor R1 such that I = 50 mA. R1 =
Tries 0/6
Current Divider
In the circuit above, it is known that
Is = 2 mA R1 = 7 kΩ R2 = 2.7 kΩ R3 = 3.3 kΩ
Find the current through resistors R2 and R3:
mA
I=
Tries 0/6
Ω
Chris Schmitz - ECE 110 Spring 2015
HW4
12
Current Divider
In this problem, it may help to first establish which resistors are truly in parallel.
In the circuit above, it is known that:
Is1 = 3 A Is2 = 1 A R1 = 10 Ω R2 = 6 Ω R3 = 3 Ω
Use the current divider rule to find I1.
A
I1 =
Tries 0/6
This homework exercise is a review on sine and cosine functions. In this ECE class you will need to
use sine and cosine waves a lot.
The general form of a sine (or cosine) function is:
where A is the amplitude of the sinusoid. The angular frequency ω (measured in radians) = 2πf (that is 2 pi f). The
frequency f, measured in hertz (Hz) or cycles/second, and the period T, measured in seconds, are related according to
.
Chris Schmitz - ECE 110 Spring 2015
HW4
13
a) Given the sine function x(t) = 13 sin(15πt), answer the following questions: .......(π is pi!)
i) What is the amplitude of the function?
ii) What is the frequency of the function?
Hz
Tries 0/6
iii) What is the period of the function?
iv) How many cycles are there in 3 seconds?
s
Cycles
Tries 0/6
b) A cosine function has a period of 0.11111 and an amplitude of 17. Fill in the blanks to form the correct equation:
cos(
πt) .......(π is pi!)
You are correct. Your receipt no. is 160-5632
Note: the symbol π is the mathematical value pi (about 3.14).
What is the rms voltage of V1=100 cos (120 π t)
V (rms)
Tries 0/6
What is the rms voltage of V2=2*100 cos (120 π t)
V (rms)
Tries 0/6
4
3
2
V3(V)
1
0
−1
−2
−3
−4
−2
−1.5
−1
−0.5
0
0.5
1
time (s)
What is the rms voltage of this function, V3?
V (rms)
Tries 0/6
1.5
2
Chris Schmitz - ECE 110 Spring 2015
HW4
14
V1(t) is a square wave that goes from 0 to 5 V with 60% duty cycle.
V (rms)
What is the rms voltage of V1?
Tries 0/6
V2(t) is a square wave that goes from 0 to 10 V with 60% duty cycle.
V (rms)
What is the rms voltage of V2?
Tries 0/6
V3(t) is a square wave that goes from 0 to 10 V with 30% duty cycle.
V (rms)
What is the rms voltage of V3?
P (Watts)
Tries 0/6
7
6
5
4
3
2
1
0
−1
−5
0
5
10
15
20
time (s)
The graph above shows two complete periods of a certain power profile (it goes on forever in both directions). The
graph is drawn to scale. Answer these questions about this waveform:
What is the maximum height of the graph (in Watts)?
W
Tries 0/6
What is the period for the function?
s
Tries 0/6
What is the average value of this function?
W
V1 (Volts)
Tries 0/6
10
5
0
−5
−10
0
10
20
time (s)
30
40
50
The graph above shows nearly two periods of a certain periodic signal (it goes on forever in both directions). The
graph is drawn to scale. Answer these questions about this signal:
What is the period for the function?
s
Tries 0/6
What is the RMS value of this function?
Vrms
Chris Schmitz - ECE 110 Spring 2015
HW4
15
for the voltage source: Vs = 1.2 V, R = 250 Ω, and for the current source: Is = 55 mA.
Find the values of power that describe each element.
ing/absorbing.
mW
For the voltage source, PV=
For the resistor, PR=
Be sure to include the proper sign to indicated deliver-
mW
mW
For the current source, PI=
Tries 0/6
For the voltage source, Vs = 2.6 V, R = 150 Ω, and for the current source, Is = 55 mA.
Find the values of power that describe each element.
ing/absorbing.
mW
For the voltage source, PV=
For the resistor, PR=
For the current source, PI=
Tries 0/6
Be sure to include the proper sign to indicated deliver-
mW
mW
Chris Schmitz - ECE 110 Spring 2015
HW4
16
Assume that the current and voltage waveforms to an electric motor are periodic with a period of
t2 = 30 ms and have the form shown above in each period.
What is the average power, if t1 = 19 ms and t3 = 20 ms, V = 7 V and i = 2.363 A?
Pave =
W
Tries 0/6
(1) An unknown circuit is powered by a variable power supply (perhaps different combinations of battery cells or a
DC power supply like in the lab).
The current and voltage were measured for each configuration;
For each set, Apply Ohm’s Law to determine the effective resistance by computing the ratio V/I.
Ohms (i.e. V/A)
I1 = -3 A; V1 = -2 v; V1/I1 =
I2 = -1.5 A; V2 = 1 v; V2/I2 =
I3 = 1 A; V3 = 6 v; V3/I3 =
I4 = 2.4 A; V4 = 8.8 v; V4/I4 =
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Ohms (i.e. V/A)
Ohms (i.e. V/A)
Ohms (i.e. V/A)
Chris Schmitz - ECE 110 Spring 2015
HW4
Could the circuit be a linear circuit (i.e. is the relationship between I and V a linear relationship)?
A. Yes
B. No
Could the circuit be made of one resistor only?
A. Yes
B. No
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(2) Another circuit is powered by a variable power supply.
The current and voltage were measured for each configuration;
For each set, compute the ratio V/I.
Ohms (i.e. V/A)
I1 = -2.5 A; V1 = -12.5 v; V1/I1 =
I2 = -2 A; V2 = -10 v; V2/I2 =
Ohms (i.e. V/A)
Ohms (i.e. V/A)
I3 = -1 A; V3 = -5 v; V3/I3 =
Ohms (i.e. V/A)
I4 = 1.7 A; V4 = 8.5 v; V4/I4 =
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Is the circuit a linear circuit (i.e. is the relationship between I and V a linear relationship)?
A. Yes
B. No
Could the circuit be made of one resistor only?
A. Yes
B. No
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17
Chris Schmitz - ECE 110 Spring 2015
HW4
18
8
6
4
I (amps)
2
0
−2
−4
−6
−8
−8
−6
−4
−2
0
V (volts)
2
4
6
8
What is the open-circuit voltage of the circuit described by this IV characteristic?
V
What is the short-circuit current of the circuit described by this IV characteristic?
A
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Chris Schmitz - ECE 110 Spring 2015
HW4
19
If the i-v characteristic for the electrical component C can be described by the linear equation:
i = 0.76*v + -0.49
(Hint: Look carefully for any minus signs in the equation. They don’t show up very well.)
Find the voltage, current and power for component C, given the following connections to terminals a and b. Also
state whether component C is a source (supplying energy) or a load (dissipating energy).
a) An ideal current source <strong>I<sub>s</sub> = 0.125 A</strong> is connected to the a-b terminals as shown.
(hint: you must combine the given equation i = 0.76*v + -0.49 of circuit C with the equation of the connected
source to solve for v and i...)
v=
i=
V,
A
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P (for circuit C) =
Component C is
A. a source
B. a load
C. neither
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W
Chris Schmitz - ECE 110 Spring 2015
HW4
20
b) A 32 Ω resistor is connected to the a-b terminals as shown.
(hint: you must use the given equation i = 0.76*v + -0.49, and combine it with another equation to solve for v and
i...)
v=
V,
A
i=
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P (of circuit C) =
W
Component C is
A. a source
B. a load
C. neither
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The i-v characteristics for subcircuits C1 and C2 are graphed below.
Chris Schmitz - ECE 110 Spring 2015
HW4
21
a) From the given graph, find the numerical values for i and v, obtained when connecting the two circuits C1 and C2.
A
i=
v=
V
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b) The given i-v graph for subcircuit C1 represents the following circuit:
Using the given graph, find vs and R1:
vs =
V
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R1 =
ohms
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c) The given i-v graph for subcircuit C2 represents the following circuit (Note: since the i-v characteristic
goes through the origin (0,0), and it is linear, subcircuit C2 does not contain a source, but a resistor only):
Using the given graph, find the resistance R2: R2 =
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Chris Schmitz - ECE 110 Spring 2015
HW4
22
20
15
10
I (amps)
5
0
−5
−10
−15
−20
−20
−15
−10
−5
0
V (volts)
5
10
15
20
What is the effective (Thevenin/Norton) resistance of the circuit described by this IV characteristic?
Ω
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Consider the following Thevenin circuit:
With the following parameters:
VTh= 1.5 V, RTh= 22 Ω
Applying basic circuit laws to the above circuit with the parameter values given,
Chris Schmitz - ECE 110 Spring 2015
HW4
23
a) find the value of v when i=0 (open circuit on the right):
volts (when i=0)
v=
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b) find the value of i when v=0 (short circuit on the right):
i=
amps (when v=0)
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c) Use the previous two results, and think about the shape of the IV graph for the given circuit (draw it on paper);
check the one correct statement below:
Choices: The IV graph is increasing, The IV graph is decreasing.
• (choose one)
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d) It is a known fact that any Thevenin circuit has a linear i-v characteristic described by the equation i = a*v + b;
Give the value of the coefficients a and b in the above equation for i for the given circuit:
(hint: it is helpful to look at all the results you obtained in the previous parts)
a=
b=
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Consider the following Norton circuit:
With the following parameters:
iN= 1.5 A, RN= 22 Ω
Applying basic circuit laws to the above circuit with the parameter values given,
Chris Schmitz - ECE 110 Spring 2015
HW4
24
a) find the value of v when i=0:
v=
volts (when i=0)
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b) find the value of i when v=0:
i=
amps (when v=0)
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c) Use the previous two results, and think about the shape of the IV graph for the given circuit (draw it mentally);
check the one correct statement below:
Choices: The IV graph is increasing, The IV graph is decreasing.
• (choose one)
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d) It is a known fact that any Norton circuit has a linear i-v characteristic described by the equation i = a*v + b;
Give the value of the coefficients a and b in the above equation for i for the given circuit:
(hint: it is helpful to look at all the results you obtained in the previous parts)
a=
b=
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e) Find VTh and RTh for the Thevenin circuit below such that it has an i-v characteristic identical to the i-v
characteristic for the given Norton circuit.
Chris Schmitz - ECE 110 Spring 2015
HW4
e2) RTh =
25
Ohms
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