RLC Circuit Analysis Secure Meter Training

RLC Circuit Analysis Secure Meter Training. SHRUTI BHADVIYA Asst. Prof. EE Dept..

An example of an AC source is V(t) = vo sin(wt),.

Element Impedance.

The instantaneous current flowing through the loop being the same for each circuit element. Since the inductive and capacitive reactance’s XL and XC are a function of the supply frequency, the sinusoidal response of a series RLC circuit will therefore vary with frequency, ƒ. Then the individual voltage drops across each circuit element of R, L and C element will be “out-of-phase” with each other..

The instantaneous voltage across a pure resistor, VR is “in-phase” with current. The instantaneous voltage across a pure inductor, VL “leads” the current by 90o. The instantaneous voltage across a pure capacitor, VC “lags” the current by 90o. Therefore, VL and VC are 180o. “out-of-phase” and in opposition to each other..

The amplitude of the source voltage across all three components in a series RLC circuit is made up of the three individual component voltages, VR, VL and VC with the current common to all three components..

Resistance ( - in-phase- ). 900 1 Inductance ( -ELI-).

Instantaneous Voltages for a Series RLC Circuit. The phasor diagram for a series RLC circuit is produced by combining together the three individual phasors above and adding these voltages vectorially..

Since the current flowing through the circuit is common to all three circuit elements we can use this as the reference vector with the three voltage vectors drawn relative to this at their corresponding angles. The resulting vector VS is obtained by adding together two of the vectors, VL and VC and then adding this sum to the remaining vector VR. The resulting angle obtained between VS and i will be the circuits phase angle..

Vs. Above that the voltage vectors produce a rectangular triangle comprising of : hypotenuse VS horizontal axis VR vertical axis VL – VC The Voltage Triangle: use Pythagoras’s theorem on this voltage triangle to mathematically obtain the value of VS..

vu-vc. The current has the same amplitude and phase in all the components of a series RLC circuit. Then the voltage across each component can also be described mathematically according to the current flowing through, and the voltage across each element as..

By substituting these values into the Pythagoras equation for the voltage triangle will give us:.

The amplitude of the source voltage is: proportional to the amplitude of the current flowing through the circuit. This proportionality constant is called the Impedance of the circuit which ultimately depends upon: the resistance the inductive capacitive reactance..

In the series RLC circuit, it can be seen that the opposition to current flow is made up of three components, XL, XC and R with the reactance. XT of any series RLC circuit being defined as: XT = XL – XC or XT = XC – XL whichever is greater..

The impedance Z of a series RLC circuit depends upon the angular frequency, ω If the capacitive reactance is greater than the inductive reactance XC > XL then the overall circuit reactance is capacitive giving a leading phase angle. If the inductive reactance is greater than the capacitive reactance XL > XC then the overall circuit reactance is inductive giving the series circuit a lagging phase angle..

If the two reactance’s are the same XL = XC Then the angular frequency at which this occurs is called the resonant frequency and produces the effect of resonance. The magnitude of the current depends upon the frequency applied to the series RLC circuit. When impedance, Z is at its maximum, the current is a minimum and likewise, when Z is at its minimum, the current is at maximum..

The phase angle, θ between the source voltage, VS and the current, I is the same as for the angle between Z and R in the impedance triangle. This phase angle may be positive or negative in value depending on whether the source voltage leads or lags the circuit current and can be calculated mathematically from the ohmic values of the impedance triangle as:.

parallel rlc circuit. Parallel RLC Circuit. The resistor, inductor, and capacitor are all connected across the same voltage supply but operate independently, with the voltage constant across each and the total current split among them..

vector diagram of rlc circuit. The total current drawn from the supply is equal to its vector sum of all the currents, as the current flowing in resistor, inductor and capacitor are not in the same phase with each other..

Phasor diagram of parallel RLC circuit, IR is the current flowing in the resistor, R in amps. IC is the current flowing in the capacitor, C in amps. IL is the current flowing in the inductor, L in amps. Is is the supply current in amps..

In the parallel RLC circuit, all the components are connected in parallel; so the voltage across each element is same. Therefore, for drawing phasor diagram, take voltage as reference vector and all the other currents i.e. IR, IC, IL are drawn relative to this voltage vector. The current through each element can be found using Kirchhoff’s Current Law, which states that the sum of currents entering a junction or node is equal to the sum of current leaving that node..

Z of a parallel RLC circuit; each element has reciprocal of impedance (1 / Z) i.e. admittance, Y. So in parallel RLC circuit, it is convenient to use admittance instead of impedance..

In a circuit containing inductor and capacitor, the energy is stored in two different ways. When a current flows in a inductor, energy is stored in magnetic field. When a capacitor is charged, energy is stored in static electric field..

Resonant Frequency. During resonance, at certain frequency called resonant frequency, fr..