16) i. Determine the value of phase difference between the current and the voltage in given series  L-C-R circuit.



ii. Calculate the value of additional capacitor which may be joined suitably to capacitor C that would make the power factor of the circuit unity.

Dear Student,

In LCR circuits both internal (inductor) resistance, and external resistance are present in the complete circuit. Therefore, it will be easier to consider that the voltage VR is the voltage across the TOTAL circuit resistance, which comprises the internal resistance of L, added to any separate fixed resistor. Where VS is mentioned, this is the applied supply voltage.

The phase relationship between the supply voltage VS and the circuit current IS depends on the relative values of inductance and capacitance, and whether the inductive reactance (XL) is greater or less than the capacitive reactance (XC). There are various conditions possible, which can be illustrated using phasor diagrams.



or,  

given that,V=V0(sin1000t+φ) comparing with standard form we seeω=1000XL=ωLXL=100 ΩXC=1ωCXC=500 ΩR=400 Ωor,  φ=tan-1100-500400 φ=tan-1(-1)φ=-π4 (φ=-45°)

Power Factor=RZgiven,Final Power factor is 1 thus we have,  Z=Ror,  R=R2+XL-XC2or,  XL=XC  ( Resonance condition )C'=1ω2L  or, C'=10 μFbut C'=C+CnewFor parallel connectionCnew= 8 μF

Regards.



 

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