Shown here is the cartesian form of the complex impedance. The primary circuit current is given by: For series combinations of components such as RL and RC combinations, the component values are added as if they were components of a vector. From the secondary circuit equation we can find an expression for the secondary current I S. An example of the application of resonant circuits is the selection of AM radio stations by the radio receiver. Using complex impedance is an important technique for handling multi-component AC circuits. Power in a Series Resonant Circuit The average power dissipated in a series resonant circuit can be expressed in terms of the rms voltage and current as follows: Obtaining the circuit equations requires the simultaneous solution of the primary and secondary circuit equations.

A “quality factor” Q, as described below, is a measure of that selectivity, and we speak of a circuit having a “high Q” if it is more narrowly selective. Power in a Series Resonant Circuit The average power dissipated in a series resonant circuit can be expressed in terms of the rms voltage and current as follows: The application of the voltage law to both primary and secondary circuits of a transformer gives:. The phase relation is often depicted graphically in a phasor diagram. Does it ever make sense to put capacitors in series? Phase When capacitors or inductors are involved in an AC circuit, the current and voltage do not peak at the same time. For ideal coupling, the mutual inductance becomes.

Using the forms of the inductive reactance and capacitive reactance, the term hylerphysics them can be expressed in terms of the frequency. Series Resonance The resonance of a series RLC circuit occurs when the inductive and capacitive reactances are equal in magnitude but cancel each other because they are degrees apart in phase.

If the response of the circuit is more narrowly peaked around the chosen frequency, we say that the circuit has higher “selectivity”. Does it ever make sense to put capacitors in series? Resonant circuits are used to respond selectively to signals of a given frequency while discriminating against signals of different frequencies.

### Charging a Capacitor

The selectivity of a circuit is dependent upon the amount of resistance in the circuit. In the transformer, the effect of the mutual inductance is to cause the primary ciruit to take more power from the electrical supply in response to an increased load on the secondary. For series resonance the condition of resonance is straightforward and it is characterized by minimum impedance and zero phase.

Resonance Resonance in AC circuits implies a special frequency determined by the values of the resistancecapacitanceand inductance. Index Transformer concepts Faraday’s law concepts Inductance concepts. Use of Complex Impedance The handling of the impedance of an AC circuit with multiple components quickly becomes unmanageable if sines and cosines are used to represent the voltages and currents.

The resonance of a series RLC circuit occurs when the inductive and capacitive reactances are equal in magnitude but cancel each other because they are degrees apart in phase. In the example above, you can see that maximum output power is obtained with a load resistance between 15 and 20 ohms. The basic parts of the strategy are as follows: The primary circuit current is given by: The parallel resonant circuit is more commonly used in electronics, but the algebra necessary to characterize the resonance is much more involved.

It is sometimes done in electronics practice because capacitors have maximum working voltages, and with two ” volt maximum” capacitors in series, you can increase the working voltage to volts. The primary and secondary loop equations then take the form: This depicts the phasor diagrams and complex impedance expressions for RL and RC circuits in polar form.

### Phase Relationships in AC Circuits

This can be hyperphyscs in the form of a standard AC circuit impedance Z: The application of the voltage law to both primary and secondary circuits of a transformer gives:. The sharp minimum in impedance which occurs is useful in tuning applications. The smaller the resistance, the higher the “Q” for given values of L and C.

The transformer is the most common application of the concept of mutual inductance. From the secondary circuit equation we can find an expression for the secondary current I S.

Resonance in AC circuits implies a special frequency determined by the values of the resistancecapacitanceand inductance.

For example, if the load resistance in the secondary is reduced, then the power required will increase, forcing the primary side of the transformer serifs draw more current to supply the additional need. Index AC circuit concepts. The basic parts of the strategy are as follows:. Charge on Series Capacitors. When too heavy a load is drawn from the secondary, the primary coil heats up and the amount of audible “hum” that you hear from the transformer increases.

Transformer The application of the voltage law to both primary and secondary circuits of a transformer gives: Parallel resonancewhich is more common in electronic practice, requires a more careful definition. A “quality hypephysics Q, as described below, is a measure of that selectivity, and we speak of a circuit having a “high Q” if it is more narrowly selective. A battery will transport charge from one plate to hyperphyskcs other until the voltage produced by the charge buildup is equal to the battery voltage.

The fraction of a period difference between the peaks expressed in degrees is said to be the phase difference. Selectivity and Q of serues Circuit Resonant circuits are used to respond selectively to signals of a given frequency while discriminating against signals of different frequencies.

The sharpness of the minimum depends on the value of R and is characterized by the “Q” of the circuit. When capacitors or inductors are involved in an AC circuit, the current and voltage do not peak at the same time.

Clrcuit is a practical midrange of load resistances for the operation of a transformer. The length of the phasor is proportional to the magnitude of the quantity represented, and its angle represents its phase relative to that of the current through the resistor. Impedances in this form can be used as building blocks for calculating the impedances of combination circuits like the RLC parallel circuit.

## RC Circuit

Data table and explanation. Using the same circuit parameters, the illustration at left shows the power dissipated in the circuit as a function of frequency. Note that the phase angle, the difference in phase between sereis voltage and the current in an AC circuitis the phase angle associated with the impedance Z of the circuit.

It is sometimes helpful to treat the phase as if it defined a vector in a plane.