4. Consider the RL circuit with a sinusoid voltage source shown in the diagram below. The values of the resistor, inductor, input voltage amplitude and frequency are R = 5, L = 50mH, and Vo = 10 V, respectively. The input voltage frequency w is variable. Assume that the circuit has reached steady state. Voejwt + ↑i(t) R سيد The input voltage can be described using the complex sinusoid function V(t) = Voejwt The current is given by a sinusoid with same the frequency was the input voltage, but a different magnitude and different phase. The physical voltage and current are obtained by taking the real part. In complex form, the current is given by i(t) Vo ejwt R1+jw/ The differential equation that describes the current follows from Kirchoff's voltage law, and is given by di(t) L + Ri(t) = Voejwt dt (a) (3 marks) Show that i(t) satisfies the differential equation for an RL circuit with a complex sinusoid voltage source. 2 (b) (6 marks) Use MATLAB to make threes graphs that show the real part of the current Re[i(t)] as a function of time for three different input frequencies: w = 10 rad/s, 100 rad/s, 1000 rad/s. Choose the time scale so that two full cycles are visible and label the frequency on each graph. (c) (2 marks) What do you notice about the amplitude of the current as the input voltage frequency changes?
4. Consider the RL circuit with a sinusoid voltage source shown in the diagram below. The values of the resistor, inductor, input voltage amplitude and frequency are R = 5, L = 50mH, and Vo = 10 V, respectively. The input voltage frequency w is variable. Assume that the circuit has reached steady state. Voejwt + ↑i(t) R سيد The input voltage can be described using the complex sinusoid function V(t) = Voejwt The current is given by a sinusoid with same the frequency was the input voltage, but a different magnitude and different phase. The physical voltage and current are obtained by taking the real part. In complex form, the current is given by i(t) Vo ejwt R1+jw/ The differential equation that describes the current follows from Kirchoff's voltage law, and is given by di(t) L + Ri(t) = Voejwt dt (a) (3 marks) Show that i(t) satisfies the differential equation for an RL circuit with a complex sinusoid voltage source. 2 (b) (6 marks) Use MATLAB to make threes graphs that show the real part of the current Re[i(t)] as a function of time for three different input frequencies: w = 10 rad/s, 100 rad/s, 1000 rad/s. Choose the time scale so that two full cycles are visible and label the frequency on each graph. (c) (2 marks) What do you notice about the amplitude of the current as the input voltage frequency changes?
Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter2: Fundamentals
Section: Chapter Questions
Problem 2.7P: Let a 100V sinusoidal source be connected to a series combination of a 3 resistor, an 8 inductor,...
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Question
Transcribed Image Text:4. Consider the RL circuit with a sinusoid voltage source shown in the diagram below. The values
of the resistor, inductor, input voltage amplitude and frequency are R = 5, L = 50mH,
and Vo = 10 V, respectively. The input voltage frequency w is variable. Assume that the
circuit has reached steady state.
Voejwt
+
↑i(t)
R
سيد
The input voltage can be described using the complex sinusoid function
V(t) = Voejwt
The current is given by a sinusoid with same the frequency was the input voltage, but a
different magnitude and different phase. The physical voltage and current are obtained by
taking the real part. In complex form, the current is given by
i(t)
Vo ejwt
R1+jw/
The differential equation that describes the current follows from Kirchoff's voltage law, and
is given by
di(t)
L + Ri(t)
=
Voejwt
dt
![(a) (3 marks) Show that i(t) satisfies the differential equation for an RL circuit with a
complex sinusoid voltage source.
2
(b) (6 marks) Use MATLAB to make threes graphs that show the real part of the current
Re[i(t)] as a function of time for three different input frequencies: w = 10 rad/s, 100 rad/s, 1000 rad/s.
Choose the time scale so that two full cycles are visible and label the frequency on each
graph.
(c) (2 marks) What do you notice about the amplitude of the current as the input voltage
frequency changes?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86794e1d-a025-469e-9776-3458200614a7%2Faa83085c-3226-4efe-919a-97c760a63c7b%2Ff2snwx_processed.png&w=3840&q=75)
Transcribed Image Text:(a) (3 marks) Show that i(t) satisfies the differential equation for an RL circuit with a
complex sinusoid voltage source.
2
(b) (6 marks) Use MATLAB to make threes graphs that show the real part of the current
Re[i(t)] as a function of time for three different input frequencies: w = 10 rad/s, 100 rad/s, 1000 rad/s.
Choose the time scale so that two full cycles are visible and label the frequency on each
graph.
(c) (2 marks) What do you notice about the amplitude of the current as the input voltage
frequency changes?
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