Cikin RLC na gaba: Me ke nan?

Fara da RLC circuit tare da resistor, inductor da kuma capacitor suna zama da dukkan su ke ciki. Wannan cikin yaduwa ce ta samun voltage supply, VS. Wannan parallel RLC circuit na da mafi karfin cewa series RLC circuit.

A series RLC circuit, current da ya faruwar da cikin dukkan suke iya ce da cikin resistor, inductor da kuma capacitor ya faruwar da cikin dukkan suke ita ce, amma a cikin yaduwar da suka ciki, voltage da ya faruwar da cikin har zuwa ba da ciki ita ce kuma current ya zama da tsari ga har zuwa ba da ciki saboda impedance da ke cikin har zuwa ba. Saboda haka parallel RLC circuit ana ce da take da dual relationship da series RLC circuit.

Total current, IS da aka fitowa daga supply ce da vector sum da resistive, inductive da kuma capacitive current, bai da mathematic sum da dukkan su ba, domin current da ya faruwar da cikin resistor, inductor da kuma capacitor bai da cikin dukkan suke ita ce; don haka ba za a iya hada arithmetically.

Za ku iya apply Kirchhoff’s current law, wanda ya ce sum da currents da suka faruwar da cikin junction ko node, ce da sum da current da suka faruwar da cikin wannan node, don haka muna sami,

Phasor Diagram of Parallel RLC Circuit

Idan V shine supply voltage.
IS shine total source current.
IR shine current da ya faruwar da cikin resistor.
IC shine current da ya faruwar da cikin capacitor.
IL shine current da ya faruwar da cikin inductor.
θ shine phase angle difference bayan supply voltage da current.

Don draw phasor diagram of parallel RLC circuit, voltage ta zama reference saboda voltage da ya faruwar da cikin har zuwa ba da ciki ita ce kuma dukkan currents da suka faruwar da cikin cikin suke iya ce da IR, IC, IL suka faruwar da cikin cikin su. Ana sanin cewa a cikin resistor, voltage da current suna da cikin dukkan suke ita ce; don haka za ku iya draw current vector IR a cikin dukkan suke da voltage. A cikin capacitor, current ta zama da voltage da 90o don haka, za ku iya draw IC vector leading voltage vector, V da 90o. A cikin inductor, current vector IL ta lag voltage da 90o don haka za ku iya draw IL lagging voltage vector, V da 90o. Tana da shawarar ka draw resultant of IR, IC, IL i.e current IS at a phase angle difference of θ with respect to voltage vector, V.

Simplifying the phasor diagram, we get a simplified phasor diagram on right hand side. On this phasor diagram, we can easily apply Pythagoras’s theorem and we get,

Impedance of Parallel RLC Circuit

From the phasor diagram of parallel RLC circuit we get,

Substituting the value of IR, IC, IL in above equation we get,

On simplifying,

As shown above in the equation of impedance, Z of a parallel RLC circuit each element has reciprocal of impedance (1/Z) i.e admittance, Y. For solving parallel RLC circuit it is convenient if we find admittance of each branch and the total admittance of the circuit can be found by simply adding each branch’s admittance.

Admittance Triangle of Parallel RLC Circuit

In series RLC circuit, impedance is considered, but as stated in introduction on parallel RLC circuit, it is exactly opposite to that of series RLC circuit; so in Parallel RLC circuit, we will consider admittance. The impedance Z has two components; resistance, R and reactance, X. Similarly, admittance also has two components such as conductance, G (reciprocal of resistance, R) and suspceptance, B (reciprocal of reactance, X). So admittance triangle of parallel RLC circuit is completely opposite to that of series impedance triangle.