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Series Ac Circuit

R-L Series Circuit R-C Series Circuit R-L-C Series Circuit

RL Series Circuit

• The total voltage in a series RL circuit is given by this equation:

 • VT = total voltage  

VR = voltage across resistor R  

VL = voltage across inductor L

The total voltage is NOT equal to the sum of the voltages across the resistor and inductor

   The sum of voltages is 

always greater than the sum of the voltages across the resistive and inductive components

RL Series Circuit

Calculate the value of XL: XL = 2∏fL

Calculate the total impedance:

IT = VT / Z VR = RIR , VL = XLIR Calculate the total phase angle

for the circuit: ф = tan-1(XL/ R)   

ANALYSIS of RL

• v = vm sin ωt 

•  i = Im sin ( ωt – ф )

Alternating Equation

RC Series Circuit

Analysis of RC

• The total voltage in a series RC circuit is given by this equation:

  

Here VR=IR  ,   VC=IXC

Impedence:

phase angle:                        Ø=tan-1XC/R

• v = vm sin ωt 

•  i = Im sin ( ωt + ф )

Alternating Equation

RLC Series Circuit

V2series = V2

R + (VL - VC)2

Now VR = IR, VL = IXL = IωL and VC = IXC= I/ωC. Substituting and taking the common factor I gives:

Zseries2 = R2 + (XL - XC)2

The angle by which the voltage leads the current is φ = tan-1 ((VL - VC)/VR) Substituting VR = IR, VL = IXL = IωL VC = IXC= I/ωC gives:

ANALYSIS of RLCCONDITION If XL>XC :

Phase angle Ǿ is positive Circuit is Positive

If XC>XL :

Phase angle Ǿ is Negative Circuit is Negative

Special CaseXL=XC

Circuit is purely resistive

Phase angle Ǿ=0

SOURCES • http://forum.allaboutcircuits.com/blog.php• http://www.allaboutcircuits.com/vol_1/index.

html• Book: V.K Mehta

QUESTION SESSION

• Contact: 01672462007• Country : Bangladesh