Alternating Current Capacitors and Inductors are used in a variety of AC circuits.

I t The current from a generator or the mains varies sinusoidally

AC DC How do you measure the size of the current?

I t

If the bulbs are the same brightness, the current is effectively the same.

The RMS (root mean square) current is the same as the DC current that produces the same power. To calculate it use:

30 Hz AC in a 100μF capacitor using a LabPro

AC in a Capacitor PHASE We have seen that the current “through” a capacitor and the voltage across it are out of phase by 90 0

Think back to capacitors in DC circuits. When the charge is zero, the capacitor voltage is The current onto the capacitor is zero max

When the charge is maximum, the capacitor voltage is The current onto the capacitor is maximum zero

Likewise in AC, When the capacitor voltage is zero The current onto the capacitor is max

current capacitor voltage phasor diagram

Reactance of a Capacitor Reactance of a capacitor is how much it opposes the flow of current.

Reactance of a Capacitor Increasing the capacitance decreases the reactance

Reactance of a Capacitor Increasing the frequency decreases the reactance high frequencylow frequency

RC Circuits What will the voltmeter read? 3 V 4 V V 3 V 4 V 5 V

What is the angle between the current and the supply voltage? 3 V 4 V 5 V 53 o current supply voltage

What will the capacitor voltage be? 7.1V V 10V 7.1V 10 V What is the angle between the current and the supply voltage?

Impedence Impedence is the total of the resiatance and the reactance. It is measured in … OHMS The symbol is Z R XcXc Z

What is the impedence of the circuit? 300 Ω 400 Ω 300 Ω 400 Ω 500 Ω

What is the impedence of the circuit? 300 Ω 5.3 μF 300 Ω 420 Ω f = 100Hz

AC in an Inductor An inductor always opposes ……… a change in current. It produces an EMF that always opposes the changing current.

AC in an Inductor

current VLVL VRVR VSVS The voltage across the inductor leads the current by 90 o

Reactance of an Inductor The reactance of an Inductor is how much it opposes the flow of current.

Reactance of an Inductor Increasing the inductance increases the reactance and decreases the current

Reactance of an Inductor Increasing the frequency increases the reactance high frequencylow frequency

Reason… If the frequency is higher, the current changes more rapidly. This means the flux is changing more rapidly Bigger back emf Smaller current

So you can reduce the current either by increasing the inductance of the inductor…… or increasing the frequency of the current.

ex RL Circuits What will the voltmeter read? 3 V 4 V V 3 V 4 V 5 V

What is the angle between the current and the supply voltage? 3 V 4 V 5 V 53 o current supply voltage

What will the inductor voltage be? 7.1V V 10V 7.1V 10 V What is the angle between the current and the supply voltage?

What is the impedence of the circuit? 300 Ω 400 Ω 300 Ω 400 Ω 500 Ω

What is the impedence of the circuit? 300 Ω 0.48 H 300 Ω 420 Ω f = 100Hz

Capacitors v Inductors

Reactances and frequency Inductor reactance Capacitor reactance Impedence X f

RLC circuits So what happens when we put inductors and capacitors together? Xc XLXL R

VCVC VLVL ΣVΣV

R XLXL The inductor reactance and capacitor reactance are always opposite. So they can partly (or totally) cancel)

Xc R XLXL At low frequency: Capacitor reactance big Inductor reactance small XL- Xc Z (impedence)

Xc R XLXL At high frequency: Capacitor reactance small Inductor reactance big XL- Xc Z (impedence)

Xc R XLXL At resonant frequency: Capacitor reactance equals Inductor reactance XL= Xc Z (impedence)

At resonance…. is the same as impedence equals resistance only

Xc R XLXL Z R XLXL Z R XLXL Z Low frequency resonant frequency High frequency

impedance is minimum current is max current frequency resonant frequency large impedance small current

link to RLC cct hhtm/RLC.htm

Applications of AC

The frequency of the current is set at the resonant frequency of the RLC circuit. Putting metal in the inductor increases the inductance and reduces the resonant frequency. Current decreases Current drop sets off alarm current frequency resonant frequency