Chapter 33: Alternating Current Circuits
Learning Goals
- Understand how resistors, capacitors and inductors behave in AC circuits
individually.
- Be able to analyze series RLC circuits.
- Understand power dissipation in RLC circuits.
- Understand resonance.
- Understand transformers.
The LRC circuit
A LRC circuit consist of an inductor, resistor, capacitor, and
AC voltage source all connected in series, as shown below.
The current I will either lead or lag the applied voltage V
by the angle f depending upon
whether the circuit is capacitively or inductively dominated.
Phasor Diagrams
A phasor diagram is a visual tool which can simplify the analysis
of ac circuit problems. A typical phasor diagram is shown below:
The assembly of vectors rotates ccw about the origin,
and the y components of each vector gives the instantaneous values.
Impedance
Capacitors and inductors inhibit current flow via
capacitive and inductive reactances:
These reactances are combined with true resistance using the formula
for impedance:
Phase Angle
Because of the reactive nature of inductive and capacitive
components, the applied voltage and the current are
out of phase by an angle
Resonance
The current in an ac circuit has its maximum value for the
particular driving frequency that gives the minimum impedance:
Power
The average power delivered to the circuit by the voltage
source is
where
Transformers
A transformer with NP primary turns and NS
secondary turns will transform ac voltages according to
A step-up transformer has NS > NP,
and a step-down transformer has NS < NP.
Conservation of energy requires
