In a series LCR circuit, the inductive reactance X _ L is 24 and the capacitive reactance X _ C is 12 . The resistance R in the circuit is 9 . What is the power factor of the circuit?

Step-by-step solution

The power factor of a series LCR circuit is defined as = R Z , where Z is the impedance of the circuit. The impedance Z is given by Z = R^2 + (X_L - X_C)^2 . Given R = 9 , X_L = 24 , and X_C = 12 , we calculate Z : Z = 9^2 + (24 - 12)^2 = 81 + 12^2 = 81 + 144 = 225 = 15 . The phase angle is given by = X_L - X_C R . Substituting the values, = 24 - 12 9 = 12 9 = 4 3 . Since = 4 3 , the angle is 53^ . Answer: 53^