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

Question

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

Sayantan · Accepted Answer

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=ωL⇒XL=100 ΩXC=1ωC⇒XC=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

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.

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.