A pure
LC circuit with negligible resistance oscillates at
, the same resonant frequency as an
RLC circuit. It can serve as a frequency standard or clock circuit—for example, in a digital wristwatch. With a very small resistance, only a very small energy input is necessary to maintain the oscillations. The circuit is analogous to a car with no shock absorbers. Once it starts oscillating, it continues at its natural frequency for some time.
[link] shows the analogy between an
LC circuit and a mass on a spring.
Phet explorations: circuit construction kit (ac+dc), virtual lab
Build circuits with capacitors, inductors, resistors and AC or DC voltage sources, and inspect them using lab instruments such as voltmeters and ammeters.
Section summary
The AC analogy to resistance is impedance
, the combined effect of resistors, inductors, and capacitors, defined by the AC version of Ohm’s law:
where
is the peak current and
is the peak source voltage.
Impedance has units of ohms and is given by
.
The resonant frequency
, at which
, is
In an AC circuit, there is a phase angle
between source voltage
and the current
, which can be found from
for a purely resistive circuit or an
RLC circuit at resonance.
The average power delivered to an
RLC circuit is affected by the phase angle and is given by
is called the power factor, which ranges from 0 to 1.
Conceptual questions
Does the resonant frequency of an AC circuit depend on the peak voltage of the AC source? Explain why or why not.
Suppose you have a motor with a power factor significantly less than 1. Explain why it would be better to improve the power factor as a method of improving the motor’s output, rather than to increase the voltage input.
An
RL circuit consists of a
resistor and a
3.00 mH inductor. (a) Find its impedance
at 60.0 Hz and 10.0 kHz. (b) Compare these values of
with those found in
[link] in which there was also a capacitor.
(a)
at 60.0 Hz,
at 10.0 kHz
(b) At 60 Hz, with a capacitor,
, over 13 times as high as without the capacitor. The capacitor makes a large difference at low frequencies. At 10 kHz, with a capacitor
, about the same as without the capacitor. The capacitor has a smaller effect at high frequencies.
An
RC circuit consists of a
resistor and a
capacitor. (a) Find its impedance at 60.0 Hz and 10.0 kHz. (b) Compare these values of
with those found in
[link] , in which there was also an inductor.
An
LC circuit consists of a
inductor and a
capacitor. (a) Find its impedance at 60.0 Hz and 10.0 kHz. (b) Compare these values of
with those found in
[link] in which there was also a resistor.
(a)
at 60.0 Hz,
at 10.0 kHz
(b) These values are close to those obtained in
[link] because at low frequency the capacitor dominates and at high frequency the inductor dominates. So in both cases the resistor makes little contribution to the total impedance.
To receive AM radio, you want an
RLC circuit that can be made to resonate at any frequency between 500 and 1650 kHz. This is accomplished with a fixed
inductor connected to a variable capacitor. What range of capacitance is needed?
Suppose you have a supply of inductors ranging from 1.00 nH to 10.0 H, and capacitors ranging from 1.00 pF to 0.100 F. What is the range of resonant frequencies that can be achieved from combinations of a single inductor and a single capacitor?
The lowest frequency in the FM radio band is 88.0 MHz. (a) What inductance is needed to produce this resonant frequency if it is connected to a 2.50 pF capacitor? (b) The capacitor is variable, to allow the resonant frequency to be adjusted to as high as 108 MHz. What must the capacitance be at this frequency?
An
RLC series circuit has a
resistor, a
inductor, and an
capacitor.(a) Find the circuit’s impedance at 120 Hz. (b) Find the circuit’s impedance at 5.00 kHz. (c) If the voltage source has
, what is
at each frequency? (d) What is the resonant frequency of the circuit? (e) What is
at resonance?
An
RLC series circuit has a
resistor, a
inductor, and a 25.0 nF capacitor. (a) Find the circuit’s impedance at 500 Hz. (b) Find the circuit’s impedance at 7.50 kHz. (c) If the voltage source has
, what is
at each frequency? (d) What is the resonant frequency of the circuit? (e) What is
at resonance?
An
RLC series circuit has a
resistor, a
inductor, and an
capacitor. (a) Find the power factor at
. (b) What is the phase angle at 120 Hz? (c) What is the average power at 120 Hz? (d) Find the average power at the circuit’s resonant frequency.
An
RLC series circuit has a
resistor, a
inductor, and a 25.0 nF capacitor. (a) Find the power factor at
. (b) What is the phase angle at this frequency? (c) What is the average power at this frequency? (d) Find the average power at the circuit’s resonant frequency.
An
RLC series circuit has a
resistor and a 25.0 mH inductor. At 8000 Hz, the phase angle is
. (a) What is the impedance? (b) Find the circuit’s capacitance. (c) If
is applied, what is the average power supplied?
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?