### Document

```Admin:
• Assignment 6 is complete.
• Assignment 7 is posted
• Due Monday (20th) .
• Proposed second mid-term date:
• Wednesday May 6th
• Any conflicts?
• Final is Friday May 22nd, 10:30am - 12:30am SHL 130
• Office hours cancelled today – ask me questions after
class, or by email.
Capacitors in AC circuits
No charge flows through a capacitor
A capacitor in a DC circuit acts like a break (an open circuit)
But in AC circuits charge build-up and discharge mimics a
current.
•The consequences of this are peculiar!
• Voltage and current are not in phase:
• Current leads voltage by 90 degrees
• Impedance of Capacitor decreases with increasing frequency
Capacitative reactance – use this for
calculations which are independent of phase:
1
XC =
wC
Capacitative impedance. Complex form –
use where phase dependance is important:
ZC =
1
jwC
30-7 AC Circuits with AC Source
Example 30-10: Capacitor reactance.
What is the rms current in the circuit shown if C = 1.0 μF
and Vrms = 120 V?
Calculate (a) for f = 60 Hz and then (b) for f = 6.0 x 105 Hz.
XC =
1
wC
Note: we can simply use reactance (XC) if dealing with phase
independent quantities like rms. But the answer is not valid at any
given instant in time: for that we need the impedance (ZC)
Inductors in AC circuits
vS = Asin w t
vL = L
diL
dt
Asin w t = L
diL
dt
A
A
sin w t dt = cosw t
ò
L
wL
A
A
iL =
sin(w t - 90) =
cos(w t -180)
wL
wL
VL ( jw ) = AÐ(w t - 90)
”inductive reactance”
A
XL=ωL
I L ( jw ) =
Ð(w t -180)
wL
V ( jw )
ZL = L
= w LÐ90
I L ( jw )
cos(90)  j sin(90)  j
Z L = jw L ”inductive impedance”
iL =
• Voltage and current not in phase:
• Current lags voltage by 90 degrees
• Impedance of Inductor increases with increasing frequency
Play animation
30-7 AC Circuits with AC Source
Example 30-9: Reactance of a coil.
A coil has a resistance R = 1.00 Ω and an
inductance of 0.300 H. Determine the
current in the coil if
(a)120-V dc is applied to it, and
(b) 120-V ac (rms) at 60.0 Hz is applied.
XL=ωL
Note: we can simply use reactance (XL) if dealing with phase
independent quantities like rms. But the answer is not valid at any
given instant in time: for that, we need the impedance (ZL)
What if there is more than one component?
AC circuit analysis
• Procedure to solve a problem
–
–
–
–
Identify the source sinusoid and note the frequency
Convert the source(s) to complex/phasor form
Represent each circuit element by it's AC impedance
Solve the resulting phasor circuit using standard circuit solving tools
(equivalent impedances, voltage/ current divider, KVL,KCL,Mesh,
Thevenin etc.)
– Find the real part of the solution, and write is as a function of time.
```