Batteries, Resistors, Capacitors, Resistance (Impedance) Electromotive Force (EMF); Potential difference between two points; Units: Volts; Makes current . wire, there will be a potential difference between different points along the Note that the inductance per unit length L and the capacitance per unit length C are. In order to visualize the phase relationships between the current and voltage in ac circuits, we Just as with capacitance, we can define inductive reactance.
It is easy to remember that the voltage on the capacitor is behind the current, because the charge doesn't build up until after the current has been flowing for a while. The same information is given graphically below. It is easy to remember the frequency dependence by thinking of the DC zero frequency behaviour: At DC, a capacitor is an open circuit, as its circuit diagram shows, so its impedance goes to infinity. RC Series combinations When we connect components together, Kirchoff's laws apply at any instant.
The next animation makes this clear: This may seem confusing, so it's worth repeating: This should be clear on the animation and the still graphic below: The amplitudes and the RMS voltages V do not add up in a simple arithmetical way.
Here's where phasor diagrams are going to save us a lot of work. Play the animation again click playand look at the projections on the vertical axis. Because we have sinusoidal variation in time, the vertical component magnitude times the sine of the angle it makes with the x axis gives us v t. But the y components of different vectors, and therefore phasors, add up simply: So v tthe sum of the y projections of the component phasors, is just the y projection of the sum of the component phasors.
So we can represent the three sinusoidal voltages by their phasors. While you're looking at it, check the phases.
We'll discuss phase below. Now let's stop that animation and label the values, which we do in the still figure below. So we can 'freeze' it in time at any instant to do the analysis.
The convention I use is that the x axis is the reference direction, and the reference is whatever is common in the circuit.
In this series circuit, the current is common. In a parallel circuit, the voltage is common, so I would make the voltage the horizontal axis. Be careful to distinguish v and V in this figure! Careful readers will note that I'm taking a shortcut in these diagrams: The reason is that the peak values VmR etc are rarely used in talking about AC: Phasor diagrams in RMS have the same shape as those drawn using amplitudes, but everything is scaled by a factor of 0.
The phasor diagram at right shows us a simple way to calculate the series voltage.
The components are in series, so the current is the same in both. The voltage phasors brown for resistor, blue for capacitor in the convention we've been using add according to vector or phasor addition, to give the series voltage the red arrow. By now you don't need to look at v tyou can go straight from the circuit diagram to the phasor diagram, like this: Now this looks like Ohm's law again: V is proportional to I.
Their ratio is the series impedance, Zseries and so for this series circuit, Note the frequency dependence of the series impedance ZRC: At high frequencies, the capacitive reactance goes to zero the capacitor doesn't have time to charge up so the series impedance goes to R. We shall show this characteristic frequency on all graphs on this page.
Remember how, for two resistors in series, you could just add the resistances: That simple result comes about because the two voltages are both in phase with the current, so their phasors are parallel.
Ohm's law in AC. We can rearrange the equations above to obtain the current flowing in this circuit. So far we have concentrated on the magnitude of the voltage and current.
We now derive expressions for their relative phase, so let's look at the phasor diagram again. You may want to go back to the RC animation to check out the phases in time. At high frequencies, the impedance approaches R and the phase difference approaches zero. The voltage is mainly across the capacitor at low frequencies, and mainly across the resistor at high frequencies. Of course the two voltages must add up to give the voltage of the source, but they add up as vectors.
So, by chosing to look at the voltage across the resistor, you select mainly the high frequencies, across the capacitor, you select low frequencies. This brings us to one of the very important applications of RC circuits, and one which merits its own page: The resulting v t plots and phasor diagram look like this.
It is straightforward to use Pythagoras' law to obtain the series impedance and trigonometry to obtain the phase. We shall not, however, spend much time on RL circuits, for three reasons. First, it makes a good exercise for you to do it yourself. Second, RL circuits are used much less than RC circuits. If you can use a circuit involving any number of Rs, Cs, transistors, integrated circuits etc to replace an inductor, one usually does.
The third reason why we don't look closely at RL circuits on this site is that you can simply look at RLC circuits below and omit the phasors and terms for the capacitance.Inductor basics - What is an inductor?
In such circuits, one makes an inductor by twisting copper wire around a pencil and adjusts its value by squeezing it with the fingers.
RLC Series combinations Now let's put a resistor, capacitor and inductor in series. At any given time, the voltage across the three components in series, vseries tis the sum of these: The voltage across the resistor, vR tis in phase with the current. Once again, the time-dependent voltages v t add up at any time, but the RMS voltages V do not simply add up.
Once again they can be added by phasors representing the three sinusoidal voltages.
AC circuits, alternating current electricity
Again, let's 'freeze' it in time for the purposes of the addition, which we do in the graphic below. Once more, be careful to distinguish v and V. Look at the phasor diagram: Substituting and taking the common factor I gives: Note that, once again, reactances and resistances add according to Pythagoras' law: Now let's look at the relative phase.
Setting the inductance term to zero gives back the equations we had above for RC circuits, though note that phase is negative, meaning as we saw above that voltage lags the current. Similarly, removing the capacitance terms gives the expressions that apply to RL circuits. This case is called series resonance, which is our next topic. Resonance Note that the expression for the series impedance goes to infinity at high frequency because of the presence of the inductor, which produces a large emf if the current varies rapidly.
Similarly it is large at very low frequencies because of the capacitor, which has a long time in each half cycle in which to charge up.
At resonance, series impedance is a minimum, so the voltage for a given current is a minimum or the current for a given voltage is a maximum. These are often seen on computer cables. A typical RF choke value could be 2 milli henries. Common-mode CM chokes[ edit ] A typical common-mode choke configuration. The common mode currents, I1 and I2, flowing in the same direction through each of the choke windings, creates equal and in-phase magnetic fields which add together.
This results in the choke presenting a high impedance to the common mode signal. It passes differential currents equal but oppositewhile blocking common-mode currents.
Thus, the choke presents little inductance or impedance to DM currents. Normally this also means that the core will not saturate for large DM currents and the maximum current rating is instead determined by the heating effect of the winding resistance. The CM currents, however, see a high impedance because of the combined inductance of the positive coupled windings.
CM chokes are commonly used in industrial, electrical and telecommunications applications to remove or decrease noise and related electromagnetic interference. In this case, the leakage flux, which is also the near magnetic field emission of the CM choke is low.
However, the DM current flowing through the windings will generate high emitted near magnetic field since the windings are negative coupled in this case. To reduce the near magnetic field emission, a twisted winding structure can be applied to the CM choke. A balanced twisted windings CM choke The prototype of the balanced twisted winding CM choke The difference between the balanced twisted windings CM choke and conventional balanced two winding CM choke is that the windings interact in the center of the core open window.
When it is conducting DM current, the equivalent current loops will generate inversed direction magnetic fields in space so that they tend to cancel each other. The equivalent current loops and the magnetic fields generated Measurement for near magnetic field emission[ edit ] We need to conduct a current to the inductor and use a probe to measure the near field emission. First, a signal generator, serving as a voltage source, is connected to an amplifier.
The output of the amplifier is then connected to the inductor under measurement. To monitor and control the current flowing through the inductor, a current clamp is clamped around the conducting wire.