# Phase relationship of inductance capacitance and resistance

### Series R, L, and C | Reactance And Impedance -- R, L, And C | Electronics Textbook

In electrical and electronic systems, reactance is the opposition of a circuit element to a change in current or voltage, due to that element's inductance or capacitance. The notion of reactance is similar to electrical resistance, but it differs in several respects. In phasor analysis, reactance is used to compute amplitude and phase As frequency goes up, inductive. linear elements: the capacitor and the inductor. All the methods Unlike the resistor which dissipates energy, ideal capacitors and inductors store energy The current-voltage relationship of a capacitor is dv i C dt 90 degrees out of phase. Electrical Tutorial about AC Resistance and the Properties of AC Resistance also known as Impedance in a Single Phase AC Circuit. In both cases this voltage- current (V-I) relationship is always linear in a pure resistance. pure ohmic resistance only and have negligible values of inductance or capacitance containing.

Figure below Series resistor inductor circuit: Current lags applied voltage by 0o to 90o. This combined opposition will be a vector combination of resistance and reactance. In order to express this opposition succinctly, we need a more comprehensive term for opposition to current than either resistance or reactance alone.

### Electrical reactance - Wikipedia

This term is called impedance, its symbol is Z, and it is also expressed in the unit of ohms, just like resistance and reactance. In the above example, the total circuit impedance is: To calculate current in the above circuit, we first need to give a phase angle reference for the voltage source, which is generally assumed to be zero. As with the purely inductive circuit, the current wave lags behind the voltage wave of the sourcealthough this time the lag is not as great: Figure below Current lags voltage in a series L-R circuit.

We can verify this mathematically: The voltage across the resistor has the exact same phase angle as the current through it, telling us that E and I are in phase for the resistor only.

The voltage across the inductor has a phase angle of This tells us that E and I are still 90o out of phase for the inductor only. Figure below Spice circuit: Instead of a phase angle of This is merely an idiosyncrasy of SPICE and does not represent anything significant in the circuit simulation itself. Note how both the resistor and inductor voltage phase readings match our calculations Applying a table to this simple series resistor-inductor circuit would proceed as such.

If you are using a calculator that has the ability to perform complex arithmetic without the need for conversion between rectangular and polar forms, then this extra documentation is completely unnecessary.

Since this is a series circuit, we know that opposition to electron flow resistance or impedance adds to form the total opposition: Just as with DC, the total current in a series AC circuit is shared equally by all components. Phase angles for impedance, however like those of the resistor, inductor, and capacitorare known absolutely, because the phase relationships between voltage and current at each component are absolutely defined.

Since the above example circuit is a series circuit, we know that the total circuit impedance is equal to the sum of the individuals, so: Inserting this figure for total impedance into our table: Being a series circuit, current must be equal through all components.

## Phase Shift

Thus, we can take the figure obtained for total current and distribute it to each of the other columns: Notice something strange here: How can this be? The answer lies in the interaction between the inductive and capacitive reactances. Expressed as impedances, we can see that the inductor opposes current in a manner precisely opposite that of the capacitor.

When these two contrary impedances are added in seriesthey tend to cancel each other out!

It is analogous to adding together a positive and a negative scalar number: If the total impedance in a series circuit with both inductive and capacitive elements is less than the impedance of either element separately, then the total current in that circuit must be greater than what it would be with only the inductive or only the capacitive elements there.

With this abnormally high current through each of the components, voltages greater than the source voltage may be obtained across some of the individual components!

With the exception of equations dealing with power Pequations in AC circuits are the same as those in DC circuits, using impedances Z instead of resistances R.

KVL tells us that the algebraic sum of the voltage drops across the resistor, inductor, and capacitor should equal the applied voltage from the source.