Massachusetts institute of Technology
Department of Nuclear Science and Engineering
Department of Electrical Engineering and Computer Science
22.071/6.071 - Introduction to Electronics, Signals and Measurement
Spring 2006
Homework 6
Due 3/22/06
Problem 1.
Calculate the currents i1(t) and i2(t) as shown on the following circuit
10 Ω
vs = 5cos(628t )
i1
i2
0.01mF
2H
Problem 2.
Determine the voltage Vo for the following circuit. (Hint: superposition)
+
2H
vs = 10 cos(10t )
6.071/22.071 Spring 2006, HW6
Vo 1Ω
0.01mF
is = 4sin(7t )
Problem 3.
For the circuit below, determine the Thevenin equivalent circuit seen by capacitor C.
(Hint: it helps if you work out the problem symbolically and then substitute for the
element values.)
0.01mF
is = 2sin(1000t )
100 Ω
C
2mH
0.01uF
Problem 4.
Tau finds a black box with 3 terminals labeled Χ, Υ, Ζ. Tau, who took 6.071 last year,
decides to make resistance measurements across the terminals at DC ( ω = 0 Hz ) and at
high frequency ( ω large). She observes the following results:
Resistance (Ω) at
Measure resistance across
Χ–Υ
Υ–Ζ
Χ-Ζ
DC
∞
0
∞
High-Freq.
40
∞
∞
Which of the following equivalent circuits is inside Tau’s black box?
x
C
R
x
y
R
L
y
L
C
z
z
Circuit A
x
Circuit B
R
y
x
C
y
L
L
C
R
z
Circuit C
6.071/22.071 Spring 2006, HW6
z
Circuit D
Problem 5.
A motor is made up of a coil which has a resistance R and an inductance L. We will set
up an experiment to measure the values of R and L. The circuit is shown below.
10 Ω
+
motor
Va R
Vs
+
Vm
-
L
The motor runs with 60Hz power and all measurements will be performed with the real
source power connected to it and operating at a constant load (steady state). Using a
voltmeter set in AC mode (i.e measure the RMS value of a sinusoidal voltage) we
perform the following measurements.
Vs = 220 Volts , Va = 75 Volts , Vm = 110 Volts
Use these measurements to determine R and L
6.071/22.071 Spring 2006, HW6