Lecture 10/10 Chapter 24 Flashcards
AC Circuit
o An AC circuit consists of a
combination of circuit
elements and an AC generator
or source
o The output of an AC generator
is sinusoidal and varies with
time according to the following
equation
o Δv = ΔVmax sin 2πƒt
o Δv is the instantaneous
voltage
o ΔVmax is the maximum
voltage of the
generator
o ƒ is the frequency at
which the voltage
changes, in Hz
Resistor in an AC Circuit
o The current and the voltage reach
their maximum values at the same
time
o The current and the voltage are said
to be in phase
o The direction of the current has no effect on the behavior of the resistor
o The rate at which electrical energy is dissipated in the circuit is given by
rms Current and Voltage
- The voltage and current in an ac circuit both average to zero,
making the average useless in describing their behavior. - We use instead the root mean square (rms); we square the value,
find the mean value, and then take the square root. - 120 volts is the rms value of household ac.
o The rms current is the direct current that would dissipate the same
amount of energy in a resistor as is actually dissipated by the AC current
*equation
o Alternating voltages can also be discussed in terms of rms values
*equation
rms Current and Voltage
o Many of the equations will be in the same form as in DC circuits
o Ohm’s Law for a resistor, R, in an AC circuit
o ΔVR,rms = Irms R
o Also applies to the maximum values of v
and i
o The average power dissipated in resistor in an
AC circuit carrying a current I is
℘av = (I^2(below rms)(R)
Quick Quiz
The rms current is equal to the direct current that:
a. produces the same average voltage across a resistor as in an AC circuit.
b. dissipates an equal amount of energy in a resistor at the same rate as in an AC circuit.
c. provides the same average current in a resistor as in an AC circuit.
d. results in the same peak power in a resistor as in an AC circuit.
Capacitors in an AC Circuit
o The impeding effect of a capacitor
on the current in an AC circuit is
called the capacitive reactance
and is given by
o When ƒ is in Hz and C is in F,
XC will be in ohms
o Ohm’s Law for a capacitor in an
AC circuit
o ΔVC,rms = Irms XC
Inductors in an AC Circuit
o The effective resistance of a coil in an AC circuit is called its inductive reactance and is given by
o XL = 2πƒL =ωL
o When ƒ is in Hz and L is in H, XL will be in ohms
o Ohm’s Law for the inductor
o ΔVL,rms = Irms XL
Quick Quiz
The frequency in an AC series circuit is
doubled. By what factor does this change the
capacitive reactance?
a. 1/2
b. 1/4
c. 2
d. 4
a. 1/2
The RLC Series Circuit
o The current in the circuit is the
same at any time and varies
sinusoidally with time
ΔV, net instantaneous voltage
Phasor Diagrams
- In order to visualize the phase
relationships between the current
and voltage in ac circuits, we
define phasors—rotating vectors
whose length is the maximum
voltage or current, and which rotate
around an origin with the angular
speed of the oscillating current. - The instantaneous value of the
voltage or current represented by
the phasor is its projection on the y
axis.
Phasor Diagram for RLC
Series Circuit
o The voltage across the resistor is on the
+x axis since it is in phase with the
current
o The voltage across the inductor is on the
+y since it leads the current by 90°
o The voltage across the capacitor is on the
–y axis since it lags behind the current by
90°
o The phasors are added as vectors
to account for the phase
differences in the voltages
o ΔVL and ΔVC are on the
same line and so the net
y component is ΔVL - ΔVC
o φ is the phase angle between the current and
the maximum voltage
o The equations also apply to rms values
Quick Quiz
A resistor, inductor, and capacitor are connected in series, each with effective (rms) voltage of 65 V, 140 V, and 80 V, respectively. What is the value of the effective (rms) voltage of the applied source in the circuit?
a. 48 V
b. 88 V
c. 95 V
d. 285 V
Impedance of a Circuit
o The impedance, Z, can also be represented in a phasor diagram
o Ohm’s Law can be applied to the impedance
o ΔVmax = Imax Z
o This can be regarded as a generalized form of Ohm’s Law applied to a series AC circuit
o This equation applies equally well to rms values.
RLC Circuits
At high frequencies, the capacitive
reactance is very small, while the inductive
reactance is very large. The opposite is
true at low frequencies.
Quick Quiz
An ac circuit has a 100-© resistor in series with a 4.9-µF capacitor and a 700-mH inductor. At what frequency does the circuit act like a pure resistance?
A) 0.29 MHz
B) 1.9 MHz
C) 12 MHz
D) 0.54 kHz
E) 86 Hz
E) 86 Hz
