Question

An RLC circuit has resistance R=175Ω and inductive reactance XL=367Ω. (a) Calculate the circuit's capacitive reactance XC (in Ω ) if its power factor is cos(φ)=0.707. Ω (b) Calculate the circuit's capacitive reactance XC( in Ω) if its power factor is cos(φ)=1.00. Ω (c) Calculate the circuit's capacitive reactance XC (in Ω ) if its power factor is cos(φ)=1.00×10−2. Ω [−/1 Points] SERCP11 21.6.P.037.MI. An RLC circuit is used in a radio to tune into an FM station broadcasting at f=99.7MHz. The resistance in the circuit is R=12.8Ω, and the inductance is L=1.48μH. What capacitance should be used? pF

Answer 1

In an RLC circuit, the capacitive reactance XC can be calculated using the power factor and other circuit values. When the power factor is 1.00, the circuit is purely resistive and XC is 0 Ω. When the power factor is very small, the circuit is highly capacitive and XC can be approximated based on the values of R and XL.

Step-by-step explanation:

(a) The power factor in an RLC circuit is given by the cosine of the phase angle (φ). Since the power factor is cos(φ) = 0.707, we can use this value to find the capacitive reactance XC. The formula for the power factor in terms of XC and XL is: cos(φ) = XC / √(R^2 + (XL - XC)^2). Plugging in the values for R and XL, we can solve for XC.

(b) In the case where the power factor is cos(φ) = 1.00, the circuit is purely resistive and has no reactance. Therefore, the capacitive reactance XC would be 0 Ω.

(c) When the power factor is cos(φ) = 1.00×10^−2, the circuit is highly capacitive. In this case, the capacitive reactance XC is much larger than the inductive reactance XL. Therefore, XC can be approximated as XC = √(R^2 - XL^2).