Chapter 33: AC Circuits

Alternating Current Circuits

source for image: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/accircon.html#c1

Equations to remember:

when an AC Circuit switch is closed, we have a charging circuit, and:

I = deltaV/R

voltage across the inductor equals 0, and delta V = 0

• instantaneous voltage and current are 90 degrees out of phase, where V lags behind I within the capacitor
• instantaneous voltage and current are 90 degrees out of phase, where V leads I within the Inductor
• voltage is IN PHASE With the current, within the resistor

DeltaVoltageAVG = 1/2VAVG

DeltaVrms = DeltaVmax / sqrt(2)

Inductive Reactance: XL = ωL

Capacitive Reactance: XC = 1/ωC

TOTAL reactance of an RLC circuit:

XL - XC = Rtan(theta)

theta = angle I is leading V

impedance (Z):  Impedance is ...?

Z = SQRT(R^2 + X^2)

Z = V / I

NOTE: V and I are complex sinusoidal functions for voltage and current


**when you have an AC (Oscillating voltage) Circuit that only contains an INDUCTOR,

I = Vrms / ωL

**when you have an AC (Oscillating voltage) Circuit that only contains an CAPACITOR

I = V / XC
I = VωC

The PHASE ANGLE..

in a series RLC circuit the phase angle is given by: tan(theta) = (XL - XC/R)

at resonance, Inductive Reactance equals the Capacitive Reactance:

XL = XC

Phase angles are frequency dependent~!

Power in an electric circuit

RATE OF power delivered (or work done by power) = (frequency) ( voltage)

when F and V are vectors..

P = FVcos(theta)

Quality Factor (Q)

Q tells you how underdamped an oscillator is In physics and engineering the quality factor or Q factor is a dimensionless parameter that describes how under-damped an oscillator or resonator is,^[1] or equivalently, characterizes a resonator's bandwidth relative to its center frequency.^[2] Higher Q indicates a lower rate of energy loss relative to the stored energy of the resonator; the oscillations die out more slowly

source: Wikipedia

Capacitance for an AC-circuit?

UNIT for C = FARADS (F)

C = 1/[4(pi)^2*frequency^2*(L)]