1) The document discusses alternating current (AC) circuits, including AC voltage, current, resistors, inductors, and capacitors. 2) Key concepts covered include root mean square (RMS) voltage and current values, phase relationships between voltage and current, and reactance of inductors and capacitors. 3) Reactance is the opposition to current flow in inductors and capacitors, and depends on frequency - inductive reactance increases with frequency while capacitive reactance decreases.

1. Topic 6 Alternating Current
Circuit (AC)
• Current, voltage, resistance and power for resistor in an AC circuit
• Values of peak and root mean square
• Reactance of capacitor and inductor in an AC circuit

2. AC circuits
• Alternating Current Circuits or AC circuits are simply
circuits powered by an Alternating Source, either current
or voltage.
• An Alternating Voltage or Current is one in which the
amount of either the voltage or the current alters about a
distinct mean value and reverses direction periodically.

4. AC Voltage : Vt = VmSin(t)
AC Current : It = ImSin(t)

5. Root mean square value
Irms = Imax
2
Vrms = Vmax
2

6. Values of peak and root mean square
• The RMS voltage is also known as the equivalent DC voltage because
the RMS value gives the amount of AC power drawn by a resistor
similar to the power drawn by a DC source.
• A 5Ω load connected with a 10V DC source. Power drawn =20W. (P =
V2/R)
• A 5Ω load connected with a Vrms = 10V, AC source. Power drawn
=20W. (P = Vrms
2/R)

7. Current, voltage, resistance and power for resistor in an AC circuit
= VmImsin2t

8. Because the voltage and current reach their maximum values at the same
time, they are in phase.
Ohm's law and the previous expressions for power are valid for this circuit if
the root mean square (rms) of the voltage and the rms of the current,
sometimes called the effective value, are used.
Ohm's law is expressed thus:
V R = IR,
where V R is the rms voltage across the resistor and I is the rms in the circuit.
Irms = Imax
2
Vrms = Vmax
2

9. Inductor in AC circuit
Current or voltage is lagging in the inductor
in AC circuit?
1. When voltage is applied to inductor,
for the first positive peak of the voltage
cycle (90 deg) the current at the coil will
be zero. This is due to the back emf
produced in the coil.
2. When the voltage starts to decay, the
back emf will create a current that opposes
the drop in voltage. So the current would
start to go up and reaches its peak at 180 deg
when the voltage source E=0.
At this point a steady state current is flowing
through the coil, no more back emf is
induced to oppose the current flow and
therefore, the coil acts more like a short
circuit allowing maximum current to flow
through it.
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2

10. Inductive Reactance – resistance in an inductor
Where:
• XL = Inductive Reactance in Ohms, (Ω)
• π (pi) = a numeric constant of 3.142
• ƒ = Frequency in Hertz, (Hz)
• L = Inductance in Henries, (H)
We can also define inductive reactance in radians, where Omega, ω equals 2πƒ.

12. Inductive Reactance against Frequency
Inductive reactance of a inductor
increases as the frequency of the
applied voltage increases.
Therefore, inductive reactance is
directly proportional to frequency.
As the frequency increases, the
current decreases.

13. Low pass filter
Easy passage to low-frequency signals and difficult passage to high-
frequency signals.
The inductor’s impedance
increases with increasing
frequency.
This high impedance in series
tends to block high-frequency
signals from getting to the load.

14. 3. The supply voltage begins to
decrease in a negative direction
although the voltage is still positive
down towards the zero reference line
at 180o. Capacitor starts to discharge.
This results in the capacitor current
flowing in the opposite or negative
direction.
1.A high current will start
to flow into the capacitor as
there is no charge on the
plates at t = 0.
2.As the sinusoidal
supply voltage reaches
maximum on the
waveform it becomes fully
charged, current
decreases to zero as
there is no rate of voltage
change.
4. When the supply voltage waveform
crosses the zero reference axis point at
instant 180o, the current flowing into the
capacitor is also at its maximum rate at that
instant. Also at this 180o point the capacitor
is fully discharged.
5. During the second half cycle 180o to 360o,
the supply voltage reverses direction and heads
towards its negative peak value at 270o. The
potential difference across the capacitor is at its
maximum negative value, no current flows into
the capacitor and it becomes fully charged the
same as at its 90o point but in the opposite
direction.
When the switch is closed
6.As the negative supply voltage begins to increase in
a positive direction towards the 360o point on the zero
reference line, the fully charged capacitor starts to
discharge itself until the supply voltage reaches zero at
360o at which the process of charging and discharging
starts over again. Current increases in the opposite
direction.
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6
Is the voltage or current leading
for a capacitor in an AC circuit?
Capacitor in AC circuit

15. Capacitive Reactance
Reactance – opposition to current flow in inductor or capacitor.
Capacitive reactance – reactance of a capacitor ( XC ) measured in Ohms.
XC is the Capacitive Reactance in Ohms,
ƒ is the frequency in Hertz
C is the AC capacitance in Farads, symbol F.
ω = 2πƒ

16. Capacitive Reactance against Frequency
Capacitive reactance of a capacitor
decreases as the frequency across its
plates increases.
Therefore, capacitive reactance is
inversely proportional to frequency.
As frequency increases, the capacitive reactance decreases towards zero as the
frequency increases acting like a short circuit.
Likewise, as the frequency approaches zero or DC, the capacitors reactance
increases to infinity, acting like an open circuit which is why capacitors block DC.

17. High pass filter
Only passes signal above the selected cut-off point, eliminating any low
frequency signals from the waveform.
In this circuit arrangement, the reactance of the capacitor
is very high at low frequencies so the capacitor acts like
an open circuit and blocks any input signals at VIN until the
cut-off frequency point ( ƒC ) is reached.
Above this cut-off frequency point the reactance of the
capacitor has reduced sufficiently as to now act more like
a short circuit allowing all of the input signal to pass
directly to the output as shown below in the filters
response curve.