1. AC Circuits (Chapt 33) circuits in which the currents vary in time
differential equations

2. AC Voltage
The current in any AC circuit is driven by an AC source. This alternating current varies sinusoidally with time: Δv = ΔVmax sin ωt * Δv is the instantaneous voltage
* ΔVmax is the maximum output voltage of the source * ω is the angular frequency of the AC voltage

3. AC Voltage The angular frequency is
ƒ is the frequency of the source
T is the period of the source
The voltage is positive during one half of the cycle and negative during the other half
Commercial electric power plants in Canada/US use a frequency of 60 Hz
This corresponds with an angular frequency of 377 rad/s

4. Resistors in an AC Circuit
Consider a circuit consisting of an AC source and a resistor
The AC source is symbolized by
Δv = ΔvR = Δvmaxsin wt
ΔvR is the instantaneous voltage across the resistor

5. Resistors in an AC Circuit
The instantaneous current in the resistor is
The instantaneous voltage across the resistor is also given as:
ΔvR = Imax R sin ωt

6. Resistors in an AC Circuit
The graph shows the current through and the voltage across the resistor
The current and the voltage reach their maximum values at the same time
The current and the voltage are said to be in phase

7. Resistors in an AC Circuit
For a sinusoidal applied voltage, the current in a resistor is always in phase with the voltage across the resistor
The direction of the current has no effect on the behavior of the resistor
Resistors behave essentially the same way in both DC and AC circuits

8. RMS Current and Voltage
The average current in one cycle is zero
The rms current is the average of importance in an AC circuit
rms stands for root mean square
Alternating voltages can also be discussed in terms of rms values

9. Example
Show that the RMS values for a sinusoidal function are of the max.

10. Notes About RMS Values
RMS values are used when discussing alternating currents and voltages because:
AC ammeters and voltmeters are designed to read rms values
Many of the equations that will be used have the same form as their DC counterparts

11. Example
An AC power supply produces a maximum voltage ΔVmax = 100 V. This power supply is connected to a 24.0-Ω resistor, and the current and resistor voltage are measured with an ideal AC ammeter and voltmeter, as shown below. What does each meter read? Note that an ideal ammeter has zero resistance and that an ideal voltmeter has infinite resistance.

12. Example
In the simple AC circuit shown, R = 70.0 Ω and Δv = ΔVmax sin ωt. a) If ΔvR = ΔVmax for the first time at t = 0.010 0 s, what is the angular frequency of the source? b) What is the next value of t for which ΔvR = ΔVmax?

13. Example
Show that the rms value for the sawtooth voltage shown in the figure is ΔVmax /√3.

14. Solution