# 15: Alternating-Current Circuits


In this chapter, we use Kirchhoff’s laws to analyze four simple circuits in which ac flows. We have discussed the use of the resistor, capacitor, and inductor in circuits with batteries. These components are also part of ac circuits. However, because ac is required, the constant source of emf supplied by a battery is replaced by an ac voltage source, which produces an oscillating emf.

• 15.1: Prelude to Alternating-Current Circuits
Electric power is delivered to our homes by alternating current (ac) through high-voltage transmission lines. As explained in Transformers, transformers can then change the amplitude of the alternating potential difference to a more useful form. This lets us transmit power at very high voltages, minimizing resistive heating losses in the lines, and then furnish that power to homes at lower, safer voltages.
• 15.2: AC Sources
Most examples dealt with so far in this book, particularly those using batteries, have constant-voltage sources. Thus, once the current is established, it is constant. Direct current (dc) is the flow of electric charge in only one direction. It is the steady state of a constant-voltage circuit.
• 15.3: Simple AC Circuits
In this section, we study simple models of ac voltage sources connected to three circuit components: (1) a resistor, (2) a capacitor, and (3) an inductor.
• 15.4: RLC Series Circuits with AC
An RLC series circuit is a series combination of a resistor, capacitor, and inductor connected across an ac source.
• 15.5: Power in an AC Circuit
A circuit element dissipates or produces power according to P=IVP=IV , where I is the current through the element and V is the voltage across it. Since the current and the voltage both depend on time in an ac circuit, the instantaneous power is also time dependent.
• 15.6: Resonance in an AC Circuit
In the RLC series circuit, there is a resonant frequency where the inductive reactance equals capacitive reactance. The average power versus angular frequency plot for a RLC circuit has a peak located at the resonant frequency; the sharpness or width of the peak is known as the bandwidth. The bandwidth is related to a dimensionless quantity called the quality factor. A high quality factor value is a sharp or narrow peak.
• 15.7: Transformers
The device that transforms voltages from one value to another using induction is the transformer.  A transformer basically consists of two separated coils, or windings, wrapped around a soft iron core.