### Goal: To understand AC circuits and how they apply to

```Goal: To understand AC circuits
and how they apply to resistors,
capacitors, and inductions
Objectives:
1) To learn about alternating current
2) To explore how voltages and
currents of simple AC circuits
compare to DC circuits
3) To understand Capacitors in an AC
circuit
4) To understand Inductors in an AC
circuit
What is alternating current?
• So far we have looked at what is called “direct
current”.
• That is you have a constant current with time.
• However long ago it was discovered that it was
far more efficient and useful to use a current that
varied with time.
• Alternating current fluxuates over some time
period from 0A to its maximum.
• For the home the time span of the fluxuation is
1/60th of a second (a frequency of 60 Hz).
Voltage with time
• The voltage is a sine wave.
• V(t) = Vmax * sin(wt) where w is the
angular frequency
• Actual physical frequency is f = w/2π
• And period = 1/f
Root Mean Square
• The average voltage or power is found by the
Root Mean Square. RMS is just the average of
the square.
• The square of the voltage fluxuates from 0 and
1. The average of the square of the voltage is
0.5.
• So: VRMS = Vmax / 21/2
• P = V2 / R therefore Pave = ½ Pmax
• (i.e. Pave = Vave2 / R = ½ Vmax2 / R)
• Finally the current is:
• IRMS = Imax / 21/2
DC vs AC
• DC:
• V = IR
• P = IV
•
•
•
•
•
•
•
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AC:
Vrms = Irms R
Vmax = Imax R
Vmax = Vrms * 21/2
Prms = Irms Vrms = 0.5 Imax Vmax = 0.5 Pmax
Pmax = Imax Vmax
VRMS = Vmax / 21/2
IRMS = Imax / 21/2
• And you can mix and match here…
Examples
• If the Vrms of a circuit is 5V and the
resistance is 10 Ohms then what is the:
• A) Maximum Voltage
• B) RMS Current
• C) Maximum Current
• D) RMS power
Capacitors in an AC Circuit
•
•
•
•
•
•
Q=CV
But if V changes then Q is going to change.
This means there will be a current.
I = Δq / Δt = C Δv / Δt
So, I = Imax sin(wt + π/2)
In a capacitor the current is 90 degrees out of
phase with the rest of the circuit!
• The voltage is -90 degrees out of phase.
Voltage for Capacitor
• Clearly the voltage will change with time.
• This is a problem if we want equations.
• So, what we do instead is look at the maximum
voltage.
• Vc = I Xc
• (or Vmax = Imax Xc and Vrms = Irms Xc)
• Here we have created a Resistance like term
that is called the reactance of the capacitor.
• The units of Xc will be Ohms.
• And Xc = 1/(wC) = 1/(2πf C)
• So, Xc is the effective resistance of the capacitor
in an AC circuit.
Sample
• You have a 0.01 F capacitor.
• If the angular frequency of the AC current
is 60 Hz then find:
• A) the reactance of the capacitor.
• B) If attached to a 5 Vrms power source
what is the maximum current?
Voltage for Inductor
• For an inductor V = I XL
• Here XL is the reactance of the inductor.
• And XL = w L = 2πf L
• Sample:
• You have a rms current of 5A.
• If the frequency is 60 Hz and the
Inductance is 0.2 H then what is the
maximum voltage across the inductor?
Phase
• However, for an Inductor, the current lags 90
degrees BEHIND the normal.
• So, for a resistor, current as normal.
• Capacitor, 90 degrees ahead (voltage 90
behind)
• Inductor, 90 degrees behind (voltage 90 ahead)
• So, by using a capacitor or inductor you can get
parts of your circuit to do different things at
different times!
Conclusion
• We learned that alternating current is
current that varies with time.
• We learned how to find RMS and Max
voltage, power, and currents.
• We learned how to find the reactance of
capacitors and inductors.
• We learned how to use the reactance of
capacitors and inductors in circuits to find
voltage and current.
```