Electrical reactance - Wikipedia
Current is in phase with voltage in a resistive circuit. calculations is to use scalar notation, and to handle any relevant phase relationships with trigonometry. Impedance, phase relations, resonance and RMS quantities. We introduce the voltage-current relations for resistors, capacitors and inductors .. the capacitor, so the total reactive voltage (the voltage which is 90° ahead of the current) is VL. In electrical and electronic systems, reactance is the opposition of a circuit element to a change in current or voltage, due to . That is, current will flow for an out-of-phase system, however real power at certain .. Without knowledge of both the resistance and reactance the relationship between voltage and current cannot be.
Figure below Ac source drives a purely resistive load. In this example, the current to the load would be 2 amps, RMS. The power dissipated at the load would be watts. Because this load is purely resistive no reactancethe current is in phase with the voltageand calculations look similar to that in an equivalent DC circuit. If we were to plot the voltage, current, and power waveforms for this circuit, it would look like Figure below.
Current is in phase with voltage in a resistive circuit. Note that the waveform for power is always positive, never negative for this resistive circuit. This means that power is always being dissipated by the resistive load, and never returned to the source as it is with reactive loads.
Also note that the waveform for power is not at the same frequency as the voltage or current! Rather, its frequency is double that of either the voltage or current waveforms. This different frequency prohibits our expression of power in an AC circuit using the same complex rectangular or polar notation as used for voltage, current, and impedance, because this form of mathematical symbolism implies unchanging phase relationships. When frequencies are not the same, phase relationships constantly change.
As strange as it may seem, the best way to proceed with AC power calculations is to use scalar notation, and to handle any relevant phase relationships with trigonometry. AC circuit with a purely reactive inductive load. Power is not dissipated in a purely reactive load.
AC Inductor Circuits
Though it is alternately absorbed from and returned to the source. Note that the power alternates equally between cycles of positive and negative. Figure above This means that power is being alternately absorbed from and returned to the source. If the source were a mechanical generator, it would take practically no net mechanical energy to turn the shaft, because no power would be used by the load.
The generator shaft would be easy to spin, and the inductor would not become warm as a resistor would. AC circuit with both reactance and resistance. At a frequency of 60 Hz, the millihenrys of inductance give us Now this emf is a voltage rise, so for the voltage drop vL across the inductor, we have: Again we note the analogy to Ohm's law: Remembering that the derivative is the local slope of the curve the purple linewe can see in the next animation why voltage and current are out of phase in an inductor.
Again, there is a difference in phase: The animation should make this clear.
Note how this is represented on the phasor diagram. For an inductor, the ratio of voltage to current increases with frequency, as the next animation shows. Impedance of components Let's recap what we now know about voltage and curent in linear components.
The impedance is the general term for the ratio of voltage to current. The table below summarises the impedance of the different components. 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.
- Power in Resistive and Reactive AC circuits
- Phase Shift
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.
Power in Resistive and Reactive AC circuits | Power Factor | Electronics Textbook
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.
In such circuits, one makes an inductor by twisting copper wire around a pencil and adjusts its value by squeezing it with the fingers.
AC circuits, alternating current electricity
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. 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.