Questions for Solved Problems

Solved Problems
Electric Circuits & Components
1-1
Write the KVL equation for the circuit shown.
1-2
Write the KCL equation for the principal node shown.
1-2A In the DC circuit given in Fig. 1, find (i) i1 (i) i2 and (i) i3.
1-3
1-3A
1-4
Find Iout and Vout in the network circuit shown.
For the DC circuit given in the figure, find the (i) voltage vab, and (ii) current
iL when α = 0.9 and vs = 10V.
The source voltage in the circuit is 10V and R1 = R2 = 1kΩ. Αssuming a real
circuit, with source impedance = 50Ω and impedance across the voltage meter
= 1MΩ, determine the voltage in the meter.
1-5
Find the steady state current flowing through the capacitor.
1-6 Find the input impedance of the circuit. Assume that the circuit operates at ω =
50 rad/s.
1-6A In the AC circuit given, v = 120 cos(1000t + 90 o ) , R = 15Ω, C = 83.3 μF, L =
30mH. Find find (i) iR (i) iC and (i) iL in phasor form.
1-7 Find the average power delivered from a sinusoidal voltage source of V =
110<0o> V to an impedance of Z = 10 + 8j Ω. Determine also the power factor.
1-8 In the circuit shown, find the average power supplied by the source and the
average power absorbed by the resistor.
1-9 In the circuit with the ideal transformer shown, find the voltage Vo and the
impedance as seen from the source side of the transformer.
Laplace Transforms
2-1
Derive the Laplace transform for (a) u(t), (b) e-atu(t).
2-2
Obtain the Laplace transform of f (t ) = δ(t ) + 2u (t ) − 3e −2t .
2-3
Find the inverse Laplace transform for
F ( s) = 1 +
4
5s
− 2
s + 3 s + 16
2-4
Find vo(t) in the circuit shown assuming zero initial conditions.
2-5
The output in a linear system is y(t) = 10e-t sin4t u(t) when the input is x(t) = e-t
cos4t u(t). Find the transfer function of the system and its impulse function.
2-6
Determine the transfer function of the circuit shown.
Design Problem
The US space shuttle delivers parts to build up a space station. The control
circuit is shown. The electromagnet coil L for opening and closing the cargo
door requires 0.1A before activating. The activating current is i1(t). The time
required for i1 to reach 0.1A is less than 3 seconds. Check if this condition is
satisfied for L = 1H.
Key Assumption
The two switches are thrown at t = 0 and they occur instantaneously.
Switches prior to t = 0 were in position for a long time.
Operational Amplifier
3-1
A diode has the voltage current relationship as shown. Find the current flowing
through the 100Ω resistor in the two circuits using this diode.
3-2
A 741 op amp has an open-loop voltage gain of 2 x 105 and used in the circuit
shown. Find the closed-loop gain and current io when vs = 1V.
3-3
For the inverting op amp circuit shown vi = 0.5V. Calculate (a) the output
voltage vo, and (b) the current in the 10kΩ resistor.
3-4
For the op amp circuit shown, calculate the output voltage vo.
3-5
Calculate vo and io in the op amp circuit shown.
3-6
Design an op amp circuit with inputs v1 and v2 such that vo = -5v1 + 3v2.
System Modeling
4-1
Find the electrical analogy for the mechanical system described.
4-2
Find the electrical analogy for the mechanical system described.
System Response
5-1
For the RC circuit shown, obtain the transfer function and its frequency
response. Let vs = Vmcosωt.
5-2
Determine the type of filter of the following RC circuit.
5-3
In the circuit shown, determine the type of filter (a) in stage 1, (b) in stage 2,
and (c) overall.
Sensors
6-1
A strain gage R3 is connected to the Wheatstone bridge shown. The resistors
used in the circuit have the following values at balance: R1 = 1 k Ω , R2 =
120 Ω , R3 = 120 Ω , R4 = 1 k Ω , R5 = 1 k Ω , R6 = 1 k Ω , R7 = 50 Ω , R8 = 50 Ω .
The bridge is driven by a voltage of V = 5 volts and the gage factor is 2.13. Find
(i) the meter reading value E, and (ii) the actual strain value, when R3 increases
by 1 Ω .
6-2
An accelerometer has a seismic mass of 0.05kg and a spring constant of 3 x 103
N/m. The maximum mass displacement is 0.02m. Calculate (a) the maximum
measurable acceleration, and (b) the natural frequency.
6-3
An RTD has αo = 0.005/oC, RT = 500Ω at 20oC. It is placed in a Wheatstone
bridge wherein R1 = R2 = 500Ω. R3 is a variable resistor used to null the bridge.
Find the resistance of R3 at 0oC.
6-4
A thermistor has a resistance of 3.5kΩ and a dissipation constant PD = 5mW/oC
at 20oC. It is driven by a voltage of 10V. Find the temperature rise in the
thermitor due to self-heating.
6-5
A voltage of 23.72mV is measured in a type K thermocouple at 0oC reference.
Find the temperature of the measurement junction.
Actuators
7-1
A stepper motor has 10o per step and must rotate at 250rpm. What is input pulse
rate (pulses per second) needed to operate?
7-2
A servomotor has the following performance curves. It is supposed to be able to
provide a torque of 0.4Nm from rest to carry a constant load torque of 0.1Nm at
an angular acceleration of at least 5rad/s2. The polar moment of inertia of the
rotating components is 0.05kgm2. At its typical operation, the motor should be
rotating at 1600rpm to deliver a torque and output power of at least 0.42Nm and
80Watts respectively. Determine if the motor is able to perform to these
specifications.

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