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-Parallel ac networks: R-L-C series circuit
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)
Series-Parallel ac networks: R-L-C series circuit
Ex: Determine the input impedance to the series network of Fig. 12(a). Draw the impedance diagram.
Series-Parallel ac networks: R-L series circuit
Total impedance,
,
Series-Parallel ac networks: R-L series circuit
Total impedance,
,
Series-Parallel ac networks: R-L series circuit
,
Power factor PF = cos 53.13° = 0.6 lagging where 53.13° is the phase angle between E and I