Chapter 23Alternating Current Circuits

OutlineCapacitors and Capacitive ReactanceInductors and Inductive ReactanceCircuits Containing Resistance, Capacitance, and InductanceResonance in Electric CircuitsSemiconductor Devices

1- Capacitors and Capacitive ReactanceThe resistance in a purely resistive circuit has the same valueat all frequencies.

Note: the average value of the current over one cycle is zero!iR and DVR are in phase: V = I R

Capacitors in an AC Circuit

Not in phase: the voltage lags behind the current by 90o

Example 1 A Capacitor in an AC Circuit

The capacitance is 1.50F and the rms voltage is 25.0 V. What is the rms currentwhen the frequency is (a) 100 Hz and(b) 5000 Hz?

(a) (b)

In the phasor model, the voltageand current are represented by rotating arrows (called phasors).

These phasors rotate at a frequency f.

The vertical component of the phasoris the instantaneous value of the currentor voltage.Phasor diagram

2- Inductors in an AC Circuit

Not in phase: the voltage leads the current by 90o

Phasor diagram

3- Circuits containing resistance, capacitance, and inductance

= I XL= I XC= I RPhasor diagramDirection of Current

Phasor diagram

With:

SumLeads i by 90oIn phase with i Lags behind i by 90o

Conceptual Example 4 The Limiting Behavior ofCapacitors and Inductors

The rms voltage of the generator is the same in eachcase. The values of the resistance, capacitance, andinductance are the same. The frequency of the ac generator is very near zero.

In which circuit does the generator supply more rmscurrent?

Equivalent to

Power in an AC CircuitAfter 1 cycle, capacitors and inductors do not dissipate energy. They actually store energy during the first half cycle and the same amount during the second half cycle.The only power lost is across the resistor:

4- Resonance in electric circuitsResonant frequency

5- Semiconductor devicesSemiconductor devices such as diodes and transistors are widelyused in modern electronics.

The semiconducting materials (silicon and germanium) used to make diodes and transistors are doped by adding smallamounts of an impurity element.n-type and p-type semiconductors

At the junction between the n and p materials, mobile electrons andholes combine and create positive and negative charge layers.The semiconductor diode

There is an appreciable current through the diode when the diode is forward biased.

Under a reverse bias, there is almost no current through the diode.