Chapter 2Alternating Current (AC)

Transformer

Example 2.1A step-up transformer has 25 turns on the primary coil and 500 turns on the secondary

coil. If this transformer is to produce an output of 4800 V with a 12-mA current, what input current and voltage are needed?

A 2.025

5001012 3

A

N

NII

p

ssp

V 200500

25V 4800

s

psp N

NVV

Impedance Matching

pp

sp V

N

N

RI

2

1

RN

NR

s

peq

2

Transmission of power

Alternating Current (AC) Circuits

tVV sinmax

tItR

V

R

VI sinsin max

max

Root Mean Square (rms) Values

tII 22max

2 sin

2max2

12 II av

max212 III avrms

max21 VVrms

Power in an AC circuit

tRIRIP 22max

2 sin

RIRIP rmsav22

max21

R

V

R

VP rmsav

22max

2

1

AC circuits and Impedance

1 / C L

= 2 f

Capacitors in AC circuits

C

rmsrms X

VI

L

rmsrms X

VI

Inductors in AC circuits

The resistor voltage is in phase with the current

The capacitor voltage 90o lags the current

The inductor voltage 90o leading the current

RC Circuits in AC RL Circuits in AC

2222 LRXRZ L 2

222 1

C

RXRZ C

Resonance in RLC circuits

LCCL

1or

1

LCfo 2

1

Selectivity and Q of a Circuit

Metal Detectors in AirportsThe metal detector is essentially a resonant circuit. The portal you step through is an inductor (a large loop of conducting wire) that is part of the circuit. The frequency of the circuit is tuned to the resonant frequency of the circuit when there is no metal in the inductor. When you walk through with metal in your pocket, you change the effective inductance of the resonance circuit, resulting in a change in the current in the circuit. This change in current is detected, and an electronic circuit causes a sound to be emitted as an alarm.