In a series L-R circuit, XL = R and power factor of the circuit is P1 When a capacitor - Physics - Alternating Current

Question

In a series L-R circuit, XL = R and power factor of the
circuit is P1 When a capacitor with capacitance C such
that XL = XC is put in series, the power
factor becomes P2 Find P1/ P2

Domi Baruah · Accepted Answer

In a LC-R Circuit, Impedence , Z = ( R2 +
(XL- Xc)2)1/2 and Power Factor , P
= R/Z
Case 1:-When XL = R, Z =
(2R2)1/2 = (2)1/2R and
so P1= R/ (2)1/2R =>
P1= 1/ (2)1/2
Case 2 :- WHen XL = XC, Z = R AND SO Power
Factor P2 = R/R = 1
So Ratio is P1 : P2 = 1/(2)1/2
: 1

In a series L-R circuit, XL = R and power factor of the circuit is P1. When a capacitor with capacitance C such that XL = XC is put in series, the power factor becomes P2. Find P1/ P2 .

In a series L-R circuit, X_L = R and power factor of the circuit is P₁. When a capacitor with capacitance C such that X_L = X_C is put in series, the power factor becomes P2. Find P₁/ P₂ .