31.59. In an L . R-C series circuit the magnitude of the phase angle is 54.0^∘ , with the source

31.59. In an L . R-C series circuit the magnitude of the...

Key Concepts

Series RLC Circuit

A series RLC circuit is a configuration in AC circuits where a resistor, an inductor, and a capacitor are connected in a single loop. The behavior of the circuit is characterized by each component’s opposition to current: the resistor dissipates energy as heat, the inductor stores energy in a magnetic field, and the capacitor stores energy in an electric field. The overall response of the circuit to a sinusoidal input depends on the combined effects of these components.

Impedance

Impedance is the total opposition offered by a circuit to the flow of alternating current. It is a complex quantity that combines resistance (the real part) and reactance (the imaginary part), and it is expressed in ohms (?). The magnitude of the impedance determines the relationship between the applied voltage and the resulting current in an AC circuit.

Reactance

Reactance refers to the opposition to the change in current flow offered by inductors and capacitors in an AC circuit. Inductive reactance increases with frequency, while capacitive reactance decreases with frequency. This attribute causes current and voltage to be out of phase in circuits that contain these components.

Phase Angle in AC Circuits

The phase angle in an AC circuit indicates the lead or lag between the current and voltage waveforms. It arises due to the presence of reactance which causes a shift between the peaks of the voltage and current. The phase angle is crucial for understanding the timing differences in energy storage and dissipation within the circuit.

Average Power in AC Circuits

Average power in AC circuits is the time-averaged product of voltage and current over one complete cycle, taking into account the phase angle between them. This power, often termed real or active power, represents the actual energy consumed or delivered by the circuit. It is calculated using the rms values of current and voltage along with the cosine of the phase angle.

Root Mean Square (RMS) Quantities

RMS (Root Mean Square) values for voltage and current provide a measure of their effective or equivalent DC values in an AC circuit. These values are used in power calculations to account for the varying nature of sinusoidal waveforms, ensuring that the computed power reflects the actual energy transfer in the circuit.

Transcript

00:01 Hi friends here it is given then lrc parallel circuit lr and c parallel circuit are connected across the ac source having the constant amplitude of voltage but variable frequency so here v0 is constant but omega is variable in part a we have to calculate peak value of voltage across register capister and inductor as a function of omega in b part graph between i0 r i not c and i not l let me correct it this is inductor versus omega for peak voltage of ac source 100 volt resistance of 200 oinductance of 200 and capacitance of 200 and capacitance of 0 .5 micro ferret in c part discuss the behavior of iel and ic in limits of omega 0 to infinity and d part find a resonance frequency omega not and draw phaser diagram in e part amplitude of source current at omega is called to omega not f we have to find i not r i not c and i not n at omega let us start solving it starting with part a amplitude of current through the register is called to amplitude of voltage divided by resistance amplitude of current through the capacitor amplitude of voltage upon its reactance and a reactance is one upon omega c you will get v not omega c and amplitude of current through the inductor same v0 upon reactance of inductor so you will get v0 omega l so these are the three answer for part a now in part b you have to draw the graph so that we will do later on in the last now see in c for frequency to be zero current through the capacitor is zero but current through the inductor is infinite value and for omega is called to infinity current through the capacitor is infinite and across inductor it becomes zero in deep part resonance frequency is 1 upon root of lc inductance is given to capacitance is 0 .5 micro ferret so you will get this should be thousand radian per second you can find the frequency also omega upon omega not upon two pi that is thousand radian upon two into three point one four so resonance frequency you will get 159 hertz this is the answer of d part in e amplitude of source current i not r i square i not c my minus i0l whole square substitute the value b yr square plus v omega c minus b upon omega l whole square so its amplitude will be substitute the value you will get hundred upon 200 whole square 100 in 2000 c is 0 .5 micro v is 100 upon 1 ,000 into 2...

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