Series parallel ac rlc networks

Series-Parallel ac networksR-L-C series

circuit

Series-Parallel ac networks: R-L-C series circuit

Series configuration

• Current is the same through each element • Current is determined by Ohm’s law

Total impedance of a system is the sum of the individual impedances


Series configuration

Total impedance Current

Voltage across each element and

KVL or

Power θT is the phase angle between E and I

Series-Parallel ac networks: R-L series circuit

Resistance and Inductance (R-L) in series,

Z1 = R and Z2 = j XL = j ωL

Then, ZT = R + j XL = R + j ωL

So, the magnitude of the total impedance, ZT = √(R2 + XL2)

and the phase angle, θT = tan-1 (XL/R)

Therefore, (Impedance)2 = (Resistance)2 + (Reactance)2

and tan (θT) = (Reactance) / (Resistance)

Series-Parallel ac networks: R-C series circuit For a series resistance and capacitance (R-C) circuit,

Z1 = R and Z2 = 1/(jXC) = -j/ωC

Then, ZT = R - j XC = R - j /ωC

So, the magnitude of the total impedance, ZT = √(R2 + XC2)

and the phase angle, θT = tan-1 (-XC/R)

Therefore, (Impedance)2 = (Resistance)2 + (Reactance)2

and tan (θT) = (- Reactance) / (Resistance)

Series-Parallel ac networks: R-L-C series circuit Series resistance, inductance and capacitance (R-L-C) circuit,

Z1 = R, Z2 = j XL = j ωL and Z3 = 1/(jXC) = -j/ωC

Then, ZT = R + j XL - j XC = R + j ωL - j /ωC

= R + j (XL - XC) = R + j (ωL - 1/ωC)

So, the magnitude of the total impedance, ZT = √(R2 + (XL - XC)2

and the phase angle, θT = tan-1 [(XL – XC)/R]

Therefore, (Impedance)2 = (Resistance)2 + (Total Reactance)2

and tan (θT) = (Total reactance Reactance) / (Resistance)


Ex: Determine the input impedance to the series network of Fig. 12(a). Draw the impedance diagram.


Total impedance,

,


Total impedance,

,


,

Power factor PF = cos 53.13° = 0.6 lagging where 53.13° is the phase angle between E and I

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Series parallel ac rlc networks