AC electric circuits 1.More difficult than DC circuits 2. Much more difficult than DC circuits 3. You can do it!

DC: Direct current AC: Alternating current: amplitude and direction vary with time. There are many situations where working with AC is more effective. For example, AC signal can be stepped up or down using a transformer. (Amp—Speakers)

AC voltage over time To measure the voltage: Peak voltage depends on peak shape. AC is not necessarily sine waves

AC signal of various forms and looks

RMS: Root mean square value For a sine wave

AC Phase Two signals out of step with each other A leads B by 45 degrees

AC resistor circuits Voltage and current in phase

Power = I V, always positive. Resistors always consumes energy

AC Inductor circuits In AC circuits, it is not enough just to state the magnitude of a current or a voltage

We need to know the timing of the signals. A useful way to illustrate the timing, is the Use of phasor diagrams. ILIL ELEL 90 degrees AC Inductor circuits AC resistor circuits IRIR ERER

Current lags voltage by 90 degrees

The instantaneous power can be negative! i.e. The inductor absorbs power, as well as releases power.

When I and V are both positive, P is positive. When I and V are both negative, P is also positive. Since I and V are 90 degrees out of phase, There are times when one of them is positive, the other is negative, thus P is negative. When P is positive, inductor absorbs power, when P is negative, it releases power.

For a pure inductive circuit, the average power consumption is Zero Compare with R, which passively consumes power, L is a reactive load.

Voltage amplitude across the inductor is proportional to the angular frequency. The “reactance” of an inductor: High , faster change in current, Hence higher voltage. Unit  or

The reactance has two important components: 1) Its magnitude: Which relates the amplitude of the current to that of the voltage. 2) It controls the phase difference between the current and the voltage.

Reactance of L: X L =  This is the amplitude of current X L has a magnitude L , and carries a phase 90 degrees

Compare with resistance, The inductance is an active component. The amplitude and the phase of the current are controlled by the property of L

We use j to indicate the phase of the reactance reactance R

Series resistor-inductor circuits Z:Impedance

Z has a magnitude as well as a phase The magnitude of Z : The phase of Z is  :

Impedance Z= R+jX L Ohm’s law for AC circuits

For the circuit We choose V has zero phase Current lags voltage by 37 degrees, less than 90 degrees for the pure inductance circuit. This is because of the effect of the resistor. RL time constant depends on R.

RL impedance phasor diagram

Parallel R-L circuits

or

AC capacitive circuits

Capacitive reactance The phase of X C is -90 degrees.

For capacitance C

Series RC

Parallel RC

Series RLC

In general, for series RLC circuits : R is independent of frequency. The imaginary part is frequency dependent, and it equals to zero when

When The impedance is purely resistive The impedance is minimum So the current flowing in the circuit reaches maximum Under such a condition, we say the circuit Is in resonance.

is the resonance angular frequency for the circuit.

When the circuit is not in resonance The magnitude of the Z T :

Resonance