Resonance in an electrical circuit is the frequency at which the capacitive reactance equals the inductive reactance. The current through and the voltage across a series resonant circuit are in phase. Through a parallel resonant circuit they are also are in phase. At resonance, the magnitude of the impedance of a circuit with a resistor, an inductor and a capacitor all in parallel is approximately equal to circuit resistance. The magnitude of the circulating current within the components of a parallel L-C circuit at resonance is at a maximum. But at the input of a parallel R-L-C circuit it is minimum. As the frequency goes through resonance the input current of a series R-L-C circuit is a maximum. Resonance can cause the voltage across reactances in series to be larger than the voltage applied to them. For questions on the exam, the half-power bandwidth of a parallel circuit for the given resonant frequency and Q is in the table below,
For questions on the exam, the resonant frequency of a series RLC circuit with given L and C values is in the table below (R is not relevant to resonance),
The term for the time required for the capacitor in an RC circuit to be charged to 63.2% of the supply voltage is one time constant. It is also the term for the time it takes for a charged capacitor in an RC circuit to discharge to 36.8% of its initial value of stored charge one time constant. A capacitor in an RC circuit is discharged to 13.5% of the starting voltage after two time constants. [.368×.368=.135]. There are two questions on the exam asking for computation of discharge time for an RC circuit and one asking for the time constant. All are really asking for the time constant of the circuit since the amount of discharge in the questions is exactly 36.8% -- one time constant. The table below shows the values in the questions and the computed results,
Current through a capacitor leads the voltage across it by 90 degrees. The voltage across an inductor leads the current through it by 90 degrees. The system often used to display the resistive, inductive, and/or capacitive reactance components of impedance is the rectangular coordinate system. The two numbers that are used to define a point on a graph using rectangular coordinates represent the coordinate values along the horizontal and vertical axes. When using rectangular coordinates to graph the impedance of a circuit, the horizontal axis represents the voltage or current associated with the resistive component. The vertical axis represents the voltage or current associated with the reactive component. If you plot the impedance of a circuit using the rectangular coordinate system and find the impedance point falls on the right side of the graph on the horizontal line, what do you know about the circuit? It is equivalent to a pure resistance. There are eight questions (one question appearing twice, is counted as two) in the exam pool that asks, either explicitly or implicitly from the choice of answers, the polar coordinate form of the impedance of a network composed of resistance and capacitive and/or inductive reactance in series. The following table shows how to do those calculations,
There are two questions in the exam pool that ask the impedance of a network composed of resistance and capacitive or inductive reactance in parallel. The following table shows how to do those calculations,
The system often used to display the phase angle of a circuit containing resistance, inductive and/or capacitive reactance is the polar coordinate system. There are five questions asking for the phase angle from known XC (capacitive reactance), XL (inductive reactance) and R (resistance), all measured in ohms. Computation is unnecessary since all five answers are the same phase angle - 14 degrees, and by checking if XL is greater than XC you know if the voltage leads or lags the current. The table below summarizes the logic steps required,
There is one question in the exam requiring the computation of inductive reactance based on frequency before expressing the impedance as a complex number. This table shows the calculation,
There are two questions that state the impedance of a circuit in polar coordinates as an admittance in millisiemens. Admittance is the reciprocal of impedance. Just divide the number of millisiemens into 1000 to get the impedance in ohms and change the sign of the angle from + to −, or vice versa. The table below shows this simple conversion,
In all the questions in Extra pool there is only one that calls for an impedance expressed in polar coordinates to be converted into rectangular coordinates. The conversion is shown below,
Four questions involve computing the impedance of a series circuit consisting of a resister, capacitor and/or inductor from their nominal values, operating at a given frequency and then locating correct impedance on Figure E5-2, where the horizontal axis represents resistance and the vertical axis reactance. Note that inductive reactance XL is positive and capacitive reactance XC is negative. Resistance is always positive so neither Point 5 nor Point 7 is an acceptable answer. The following table summarizes the computations,
The phenomenon that as frequency increases, RF current flows in a thinner layer of the conductor, closer to the surface, is called the skin effect. Because of skin effect the resistance of a conductor is different for RF currents than for direct currents. A capacitor is a device used to store electrical energy in an electrostatic field. The unit that measures electrical energy stored in an electrostatic field is the Joule. A magnetic field is the region surrounding a magnet through which a magnetic force acts. The strength of a magnetic field around a conductor is determined by the amount of current. The magnetic field oriented about a conductor in relation to the direction of electron flow is in a direction determined by the left-hand rule. The term for energy stored in electromagnetic or electrostatic fields is potential energy. The term for an out-of-phase, nonproductive power associated with inductors and capacitors is reactive power. Reactive power is wattless, nonproductive power. In a circuit that has both inductors and capacitors, the reactive power is repeatedly exchanged between the associated magnetic and electric fields, but is not dissipated. Given the phase angle between the voltage and current, there are three questions on the exam asking for the power factor of a R-L circuit. The mathematical answer is Trigonometric Cosine of the phase angle. A Math calculator can give you the answer but if you know how to use one, you probably have the values for 30°, 45° and 60° memorized. The table below gives the values,
The true power in an AC circuit where the voltage and current are out of phase is determined by multiplying the apparent power times the power factor. There are three questions in the exam asking to compute the power consumed in a circuit with a known power factor. The table below summarizes these calculations,
The power consumed in a circuit consisting of a 100 ohm resistor in series with a 100 ohm inductive reactance drawing 1 ampere is 100 Watts. |