Parallels 13 tutorial series#

So an AC parallel circuit can be easily analysed using the reciprocal of impedance called Admittance.ДЄdmittance is the reciprocal of impedance given the symbol, Y.

Parallels 13 tutorial series#

However, the analysis of parallel RLC circuits is a little more mathematically difficult than for series RLC circuits when it contains two or more current branches. Parallel RLC networks can be analysed using vector diagrams just the same as with series RLC circuits. Since the supply voltage is common to all three components it is used as the horizontal reference when constructing a current triangle. In a parallel RLC circuit containing a resistor, an inductor and a capacitor the circuit current I S is the phasor sum made up of three components, I R, I L and I C with the supply voltage common to all three. Phase Angle, ( П† ) between the resultant current and the supply voltage: Current through capacitor, C ( I C ):ДЎ2). Current through resistance, R ( I R ):Д¦). Also construct the current and admittance triangles representing the circuit. Calculate the total current drawn from the supply, the current for each branch, the total impedance of the circuit and the phase angle. In an AC circuit, the resistor is unaffected by frequency therefore RВ =В 1kО©ДЄ 50О© resistor, a 20mH coil and a 5uF capacitor are all connected in parallel across a 50V, 100Hz supply. Calculate the impedance of the parallel RLC circuit and the current drawn from the supply. In polar form this will be given as:ДЄ 1kО© resistor, a 142mH coil and a 160uF capacitor are all connected in parallel across a 240V, 60Hz supply. Phasor Diagram for a Parallel RLC CircuitДЄs the admittance, Y of a parallel RLC circuit is a complex quantity, the admittance corresponding to the general form of impedance Z = R + jX for series circuits will be written as Y = G вЂ“ jB for parallel circuits where the real part G is the conductance and the imaginary part jB is the susceptance. The resulting angle obtained between V and I S will be the circuits phase angle as shown below. The resulting vector current I S is obtained by adding together two of the vectors, I L and I C and then adding this sum to the remaining vector I R. Since the voltage across the circuit is common to all three circuit elements we can use this as the reference vector with the three current vectors drawn relative to this at their corresponding angles.

The phasor diagram for a parallel RLC circuit is produced by combining together the three individual phasors for each component and adding the currents vectorially. Like the series RLC circuit, we can solve this circuit using the phasor or vector method but this time the vector diagram will have the voltage as its reference with the three current vectors plotted with respect to the voltage. The total current drawn from the supply will not be the mathematical sum of the three individual branch currents but their vector sum. The current flowing through the resistor, I R, the current flowing through the inductor, I L and the current through the capacitor, I C.Д«ut the current flowing through each branch and therefore each component will be different to each other and also to the supply current, I S. In the above parallel RLC circuit, we can see that the supply voltage, V S is common to all three components whilst the supply current I S consists of three parts.