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