Transcript Sinusoidal response of circuits i(t)

Sinusoidal response of circuits
J1
Key = Space
R
1kOhm
V1
i(t)
120 V
60 Hz
0Deg
L
1mH
The switch is closed at t = 0.
Determine the current i(t) for t >= 0.
ECE 201 Circuit Theory I
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Write KVL around the loop
J1
Key = Space
R
1kOhm
V1
i(t)
120 V
60 Hz
0Deg
L
1mH
di
L  R i  V cos(t   )
dt
m
ECE 201 Circuit Theory I
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The complete solution
di
L  Ri  Vm cos(t   )
dt
...
i
Vm
R 2   2 L2
1   L 
  tan 

R


cos(   )e
R
 t
L

Vm
R 2   2 L2
ECE 201 Circuit Theory I
cos(t     )
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di
L  Ri  Vm cos(t   )
dt
...
i
Vm
R 2   2 L2
1   L 
  tan 

 R 
cos(   )e
“Transient” solution
R
  t
L

Vm
R 2   2 L2
cos(t     )
“Steady-State” solution
(This is what we study now)
ECE 201 Circuit Theory I
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Steady-state solution
Vm
R  L
2
2 2
cos(t     )
• 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
ECE 201 Circuit Theory I
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Vm
R  L
2
2 2
cos(t     )
Solve for these
ECE 201 Circuit Theory I
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