Voltage and Current Phase Relationships in an Inductive Circuit
At resonance the total impedance of circuit becomes only resistive. In case of resistance Voltage and current always remains in phase so there will be zero. Any change in current in a coil (either a rise or a fall) causes a corresponding change of the magnetic flux around the coil. Because the current. This then produces an angular shift or Phase Difference between the two sinusoidal waveforms. Any sine wave that does not pass through zero at t = 0 has a phase shift. In other words phase shift is the lateral difference between two or more waveforms along a common axis and.
The angular frequency is related to the frequency, f, by: Vo represents the maximum voltage, which in a household circuit in North America is about volts. We talk of a household voltage of volts, though; this number is a kind of average value of the voltage.
The particular averaging method used is something called root mean square square the voltage to make everything positive, find the average, take the square rootor rms.
Voltages and currents for AC circuits are generally expressed as rms values.
Three-phase Y and Delta Configurations
For a sine wave, the relationship between the peak and the rms average is: In a circuit which only involves resistors, the current and voltage are in phase with each other, which means that the peak voltage is reached at the same instant as peak current. In circuits which have capacitors and inductors coils the phase relationships will be quite different.
Capacitance in an AC circuit Consider now a circuit which has only a capacitor and an AC power source such as a wall outlet. A capacitor is a device for storing charging. To understand why this is, we should review some of the relevant equations, including: We should follow the circuit through one cycle of the voltage to figure out what happens to the current. Step 1 - At point a see diagram the voltage is zero and the capacitor is uncharged.
Initially, the voltage increases quickly. The voltage across the capacitor matches the power supply voltage, so the current is large to build up charge on the capacitor plates.
The closer the voltage gets to its peak, the slower it changes, meaning less current has to flow. When the voltage reaches a peak at point b, the capacitor is fully charged and the current is momentarily zero. Step 2 - After reaching a peak, the voltage starts dropping. The capacitor must discharge now, so the current reverses direction.
When the voltage passes through zero at point c, it's changing quite rapidly; to match this voltage the current must be large and negative. Step 3 - Between points c and d, the voltage is negative. Charge builds up again on the capacitor plates, but the polarity is opposite to what it was in step one.
Again the current is negative, and as the voltage reaches its negative peak at point d the current drops to zero. Step 4 - After point d, the voltage heads toward zero and the capacitor must discharge. When the voltage reaches zero it's gone through a full cycle so it's back to point a again to repeat the cycle.Relationship of Line and Phase Voltages and Currents in a Star Connected System
The larger the capacitance of the capacitor, the more charge has to flow to build up a particular voltage on the plates, and the higher the current will be. The higher the frequency of the voltage, the shorter the time available to change the voltage, so the larger the current has to be.
The current, then, increases as the capacitance increases and as the frequency increases. Usually this is thought of in terms of the effective resistance of the capacitor, which is known as the capacitive reactance, measured in ohms.
There is an inverse relationship between current and resistance, so the capacitive reactance is inversely proportional to the capacitance and the frequency: A capacitor in an AC circuit exhibits a kind of resistance called capacitive reactance, measured in ohms.
This depends on the frequency of the AC voltage, and is given by: Note that V and I are generally the rms values of the voltage and current. Inductance in an AC circuit An inductor is simply a coil of wire often wrapped around a piece of ferromagnet.
Three-phase Y and Delta Configurations | Polyphase AC Circuits | Electronics Textbook
The reason for this has to do with the law of induction: Applying Kirchoff's loop rule to the circuit above gives: As the voltage from the power source increases from zero, the voltage on the inductor matches it. With the capacitor, the voltage came from the charge stored on the capacitor plates or, equivalently, from the electric field between the plates.
With the inductor, the voltage comes from changing the flux through the coil, or, equivalently, changing the current through the coil, which changes the magnetic field in the coil. To produce a large positive voltage, a large increase in current is required. When the voltage passes through zero, the current should stop changing just for an instant.
If the Y-connected source or load is balanced, the line voltage will be equal to the phase voltage times the square root of 3: Take close notice of the polarity for each winding in Figure below. At first glance it seems as though three voltage sources like this would create a short-circuit, electrons flowing around the triangle with nothing but the internal impedance of the windings to hold them back.
Due to the phase angles of these three voltage sources, however, this is not the case. If they do, then there will be no voltage available to push current around and around that loop, and consequently, there will be no circulating current. Starting with the top winding and progressing counter-clockwise, our KVL expression looks something like this: Indeed, if we add these three vector quantities together, they do add up to zero.
Another way to verify the fact that these three voltage sources can be connected together in a loop without resulting in circulating currents is to open up the loop at one junction point and calculate voltage across the break: Sure enough, there will be zero voltage across the break, telling us that no current will circulate within the triangular loop of windings when that connection is made complete.
Conversely, because each line conductor attaches at a node between two windings, the line current will be the vector sum of the two joining phase currents. With each load resistance receiving volts from its respective phase winding at the source, the current in each phase of this circuit will be So each line current in this three-phase power system is equal to The answer is no. With a Y-connected system, a neutral wire was needed in case one of the phase loads were to fail open or be turned offin order to keep the phase voltages at the load from changing.
This is not necessary or even possible! With each load phase element directly connected across a respective source phase winding, the phase voltage will be constant regardless of open failures in the load elements.
Even with a source winding failure, the line voltage is still V, and load phase voltage is still V. The only difference is extra current in the remaining functional source windings.