sinusoidal response of circuits
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ECE 201 Circuit Theory I 1
Sinusoidal response of circuits
V1
120 V 60 Hz 0Deg
J1Key = Space
R
1kOhm
L1mH
The switch is closed at t = 0.
Determine the current i(t) for t >= 0.
i(t)
ECE 201 Circuit Theory I 2
Write KVL around the loop
V1
120 V 60 Hz 0Deg
J1Key = Space
R
1kOhm
L1mH
i(t)
cos( )m
diL Ri V tdt
ECE 201 Circuit Theory I 3
The complete solution
2 2 2 2 2 2
1
cos( )
...
cos( ) cos( )
tan
m
Rt
Lm m
diL Ri V tdt
V Vi e t
R L R L
L
R
ECE 201 Circuit Theory I 4
“Transient” solution
“Steady-State” solution
(This is what we study now)
2 2 2 2 2 2
1
cos( )
...
cos( ) cos( )
tan
m
Rt
Lm m
diL Ri V tdt
V Vi e t
R L R L
L
R
ECE 201 Circuit Theory I 5
Steady-state solution
• Sinusoidal• The frequency is the same as the frequency
of the input signal• Maximum amplitude is different from that of
the source• Phase angle differs from that of the source
2 2 2cos( )mV t
R L
ECE 201 Circuit Theory I 6
2 2 2cos( )mV t
R L
Solve for these
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