ECEN 1400
HW 1
Resistors
ECEN 1400, Introduction to Analog and Digital Electronics HW 1: Resistors (100 pts) 1. SERIES RESISTANCES (10 PTS)
a) 5 pts: Write Ohm’s law for both resistors with voltage drops V1 and V2. Note that
current is common. Add two equations and factor out I to get something that
looks like Ohm’s law for entire circuit. Extract REQ.
V1 = IR1
V2 = IR2
V12 = V1 + V2 = IR1 + IR2 = I (R1 + R2 ) = IREQ
∴ REQ = R1 + R2
Grading:
1: Write Ohm’s law for R1
1: Write Ohm’s law for R2
1: Combine Ohm’s laws for R1 and R2
2: Do algebra and solve for Req
b) 5 pts: Substitute I from first two equations into third, solve for V1 and V2
V
V1
R
R1
V12 = IREQ = 1 REQ ∴
= 1 =
R1
V12 REQ R1 + R2
V12 = IREQ =
V2
V2
R
R2
REQ ∴
= 2 =
R2
V12 REQ R1 + R2
Note :V1 + V2 = V12
Version 1.2, 9/3/13
R1
R2
+ V12
= V12
R1 + R2
R1 + R2
R. McLeod
1
ECEN 1400
HW 1
Resistors
Grading:
1: Correctly write Ohm’s law for equivalent resistance (V12=I REQ)
1: Substitute I = V1/R1
1: Substitute I = V2/R2
1: Solve for V1 in terms of R1, R2 and V12
1: Solve for V2 in terms of R1, R2 and V12
2. PARALLEL RESISTANCES (10 PTS)
This solution uses G. You can replace G by 1/R throughout if you don’t like this.
a) 5 pts: Write Ohm’s law for both resistors with currents I1 and I2. Note that
voltage is common. Add two equations and factor out V to get something that
looks like Ohm’s law for entire circuit. Extract REQ.
I 1 = VG1
I 2 = VG 2
I 12 = I 1 + I 2 = VG1 + VG 2 = V (G1 + G2 ) = VG EQ
∴ G EQ = G1 + G2
or
1
1
1
=
+
REQ R1 R2
Grading:
1: Write Ohm’s law for R1
1: Write Ohm’s law for R2
1: Combine Ohm’s laws for R1 and R2
2: Do algebra and solve for Req
b) 5 pts: Substitute V from first two equations into third, solve for I1 and I2
I
I
G
G1
1 R1
I 12 = VG EQ = 1 G EQ ∴ 1 = 1 =
=
G1
I 12 G EQ G1 + G2 1 R1 + 1 R2
I 12 = VG EQ =
I2
I
G
G2
1 R2
G EQ ∴ 2 = 2 =
=
G2
I 12 G EQ G1 + G2 1 R1 + 1 R2
Note :I 1 + I 2 = I 12
G1
G2
+ I 12
= I 12
G1 + G2
G1 + G2
Grading:
1: Correctly write Ohm’s law for equivalent resistance (I12=V/REQ)
1: Substitute V = I1 R1
1: Substitute V = I2 R2
1: Solve for I1 in terms of R1, R2 and I12
Version 1.2, 9/3/13
R. McLeod
2
ECEN 1400
HW 1
Resistors
1: Solve for I2 in terms of R1, R2 and I12
3. PRACTICE PROBLEMS WITH OHM’S LAW (20 PTS)
a) (5 pts)
R = V / I = 80Ω
b) (5 pts)
V = I (R1 + R2 ) = 350V
c) (5 pts)
V = I R1 = 0.01[A]400Ω = 4V
I 2 = V R2 = 4 2000Ω = 2mA
d) (5 pts)
−1
REQ = (1 / R1 + 1 / R2 ) + R3 = 3 KΩ
I = 9V 3kΩ = 3mA
Grading:
1-2: Correct equation
1-2: Correct numerical answer
1: Right units including MKS prefix (K, m)
4. DESIGN PROBLEM WITH OHM’S LAW (20 PTS)
• We want to create the largest possible equivalent resistance to limit the current.
• By the voltage divider equation, R2 must be 10/50 of the total resistance and R1
must be 40/50 of the total resistance.
• R1 is thus larger than R2 and therefore must be 1MΩ
• R2 = R1 / 4 = 250 KΩ
• The current is thus I = V/REQ = 50 V / 1.25 MΩ = 40 µA
• The total power P = V I = 2 mW
Grading:
5: Recognize that this is voltage divider
5: Proper ratio of resistances (R2 = R1/4)
5: Minimize current by making R1 = 1 MOhm
3: Power dissipation, right equation
2: Power dissipation, numerically correct
Version 1.2, 9/3/13
R. McLeod
3
ECEN 1400
HW 1
Resistors
5. PRACTICE WITH RESISTOR COLOR CODES (10 PTS)
Write the value and tolerance of each resistor. 1
10Ω±10%
2.2KΩ±5%
12Ω±10%
420KΩ±10%
6.5KΩ±20%
800KΩ±5%
86KΩ±10%
770Ω±20%
4.1kΩ±10%
1Ω±10%
Grading: 1 point for each correct. Must include tolerance. Note that a leading
“black” is not standard, so on three of these, an answer of “not usual code” or
something like this would be acceptable.
1
http://www.rmroberts.com/FTP_files/ResistorColorCodeHandout.pdf
Version 1.2, 9/3/13
R. McLeod
4
ECEN 1400
HW 1
Resistors
6. USING NI MULTISIM FOR SCHEMATIC CAPTURE AND SIMULATION (30 PTS)
The plot above is made directly in multisim. The slope I/V = 1/470, confirming
Ohm’s law.
Grading:
5: Schematic including power supply and resistor
5 Voltmeter applied ACROSS resistor (in parallel)
5: Ammeter applied in series with resistor
5: Data taken correctly (simulation ran)
5: Data graphed appropriately (labels, units, sufficient points)
5: Ohm’s law verified
EXTRA CREDIT (10 PTS)
Version 1.2, 9/3/13
R. McLeod
5
ECEN 1400
HW 1
Resistors
3a (2 pts)
3b (2 pts)
3c (2pts)
3d (2 pts)
Version 1.2, 9/3/13
R. McLeod
6
ECEN 1400
HW 1
Resistors
4 (2 pts)
Grading (each):
1: Implemented circuit (correctly)
1: Showed circuit is working (show instrument panels with proper values).
Version 1.2, 9/3/13
R. McLeod
7