Although a capacitor is basically an open circuit, there is an rms current in a circuit with an AC voltage applied to a capacitor. This is because the voltage is continually reversing, charging and discharging the capacitor. If the frequency goes to zero (DC),
${X}_{C}$ tends to infinity, and the current is zero once the capacitor is charged. At very high frequencies, the capacitor’s reactance tends to zero—it has a negligible reactance and does not impede the current (it acts like a simple wire).
Capacitors have the opposite effect on AC circuits that inductors have .
Resistors in an ac circuit
Just as a reminder, consider
[link] , which shows an AC voltage applied to a resistor and a graph of voltage and current versus time. The voltage and current are exactly
inphase in a resistor. There is no frequency dependence to the behavior of plain resistance in a circuit:
Ac voltage in a resistor
When a sinusoidal voltage is applied to a resistor, the voltage is exactly in phase with the current—they have a
$\text{0\xba}$ phase angle.
Section summary
For inductors in AC circuits, we find that when a sinusoidal voltage is applied to an inductor, the voltage leads the current by one-fourth of a cycle, or by a
$\text{90\xba}$ phase angle.
The opposition of an inductor to a change in current is expressed as a type of AC resistance.
Ohm’s law for an inductor is
$I=\frac{V}{{X}_{L}}\text{,}$
where
$V$ is the rms voltage across the inductor.
${X}_{L}$ is defined to be the inductive reactance, given by
${X}_{L}=\mathrm{2\pi}\text{fL}\text{,}$
with
$f$ the frequency of the AC voltage source in hertz.
Inductive reactance
${X}_{L}$ has units of ohms and is greatest at high frequencies.
For capacitors, we find that when a sinusoidal voltage is applied to a capacitor, the voltage follows the current by one-fourth of a cycle, or by a
$\text{90\xba}$ phase angle.
Since a capacitor can stop current when fully charged, it limits current and offers another form of AC resistance; Ohm’s law for a capacitor is
$I=\frac{V}{{X}_{C}}\text{,}$
where
$V$ is the rms voltage across the capacitor.
${X}_{C}$ is defined to be the capacitive reactance, given by
${X}_{C}$ has units of ohms and is greatest at low frequencies.
Conceptual questions
Presbycusis is a hearing loss due to age that progressively affects higher frequencies. A hearing aid amplifier is designed to amplify all frequencies equally. To adjust its output for presbycusis, would you put a capacitor in series or parallel with the hearing aid’s speaker? Explain.
Would you use a large inductance or a large capacitance in series with a system to filter out low frequencies, such as the 100 Hz hum in a sound system? Explain.
High-frequency noise in AC power can damage computers. Does the plug-in unit designed to prevent this damage use a large inductance or a large capacitance (in series with the computer) to filter out such high frequencies? Explain.
Explain why the capacitor in
[link] (a) acts as a low-frequency filter between the two circuits, whereas that in
[link] (b) acts as a high-frequency filter.
(a) An inductor designed to filter high-frequency noise from power supplied to a personal computer is placed in series with the computer. What minimum inductance should it have to produce a
$\text{2.00 k\Omega}$ reactance for 15.0 kHz noise? (b) What is its reactance at 60.0 Hz?
The capacitor in
[link] (a) is designed to filter low-frequency signals, impeding their transmission between circuits. (a) What capacitance is needed to produce a
$\text{100 k\Omega}$ reactance at a frequency of 120 Hz? (b) What would its reactance be at 1.00 MHz? (c) Discuss the implications of your answers to (a) and (b).
The capacitor in
[link] (b) will filter high-frequency signals by shorting them to earth/ground. (a) What capacitance is needed to produce a reactance of
$\text{10.0 m\Omega}$ for a 5.00 kHz signal? (b) What would its reactance be at 3.00 Hz? (c) Discuss the implications of your answers to (a) and (b).
In a recording of voltages due to brain activity (an EEG), a 10.0 mV signal with a 0.500 Hz frequency is applied to a capacitor, producing a current of 100 mA. Resistance is negligible. (a) What is the capacitance? (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?
Consider the use of an inductor in series with a computer operating on 60 Hz electricity. Construct a problem in which you calculate the relative reduction in voltage of incoming high frequency noise compared to 60 Hz voltage. Among the things to consider are the acceptable series reactance of the inductor for 60 Hz power and the likely frequencies of noise coming through the power lines.
2 forces whose resultant is 100N, are at right angle to each other .if one of them makes an angle of 30 degree with the resultant determine it's magnitude
The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool that was in use in Europe, China and Russia, centuries before the adoption of the written Hindu–Arabic numeral system
a load of 20N on a wire of cross sectional area 8×10^-7m produces an extension of 10.4m. calculate the young modules of the material of the wire is of length 5m
Young's modulus = stress/strain
strain = extension/length (x/l)
stress = force/area (F/A)
stress/strain is F l/A x
El
so solve it
Ebenezer
please
Ebenezer
two bodies x and y start from rest and move with uniform acceleration of a and 4a respectively. if the bodies cover the same distance in terms of tx and ty what is the ratio of tx to ty
The atoms which form the element Cesium are known as Cesium atoms.
Naman
A material that combines with and removes trace gases from vacuum tubes.
Shankar
what is difference between entropy and heat capacity
Varun
Heat capacity can be defined as the amount of thermal energy required to warm the sample by 1°C. entropy is the disorder of the system. heat capacity is high when the disorder is high.
The quantum realm, also called the quantum scale, is a term of art inphysics referring to scales where quantum mechanical effects become important when studied as an isolated system. Typically, this means distances of 100 nanometers (10−9meters) or less or at very low temperature.
i want know physics practically where used in daily life
Vinodhini
I want to teach physics very interesting to studentd
Vinodhini
how can you build interest in physics
Prince
by reading it
Austin
understanding difficult
Vinodhini
vinodhini mam, physics is used in our day to day life in all events..... everything happening around us can be explained in the base of physics.....
saying simple stories happening in our daily life and relating it to physics and questioning students about how or why its happening like that can make
revolutionary
your class more interesting
revolutionary
anything send about physics daily life
Vinodhini
How to understand easily
Vinodhini
check out "LMES" youtube channel
revolutionary
even when you see this message in your phone...it works accord to a physics principle. you touch screen works based on physics, your internet works based on physics, etc....... check out google and search for it
revolutionary
what is mean by Newtonian principle of Relativity?
definition and explanation with example
mechanical energy is of two types 1: kinetic energy 2: potential energy,so, potential energy is actually the type of mechanical energy ,the mechanical due to position is designated as potential energy
Iram
Thank you!!!!!
Nikki
Can someone possibly walk me through this problem?
" A worker drives a 0.500 kg spike into a rail tie with a 2.50 kg sledgehammer. The hammer hits the spike with a speed of 65.0 m/s. If one-third Of the hammer's kinetic energy is converted to the internal energy of rhe hammer and spike.
Nikki
how much does the total internal energy increase
Nikki
you know the mass and the velocity of the hammer. therefore using the equation (mv^2)/2 you can find the kinetic energy. then take one third of this value and that will be your change in internal energy. here, the important thing is that spike is stationary so it does not contribute to initial Energ
Chathu
Thabk you! :)
Nikki
what is the formula for finding the to total capacitance in series arrangement
Is there a formula for time of free fall given that the body has initial velocity? In other words, formula for time that takes a downward-shot projectile to hit the ground. Thanks!