In a series RLC circuit, if the total impedance is 50Ω, the resistance is 30Ω, w
Practice Questions
Q1
In a series RLC circuit, if the total impedance is 50Ω, the resistance is 30Ω, what is the inductive reactance if the capacitive reactance is 20Ω? (2023)
10Ω
20Ω
30Ω
40Ω
Questions & Step-by-Step Solutions
In a series RLC circuit, if the total impedance is 50Ω, the resistance is 30Ω, what is the inductive reactance if the capacitive reactance is 20Ω? (2023)
Step 1: Identify the given values. We have total impedance (Z) = 50Ω, resistance (R) = 30Ω, and capacitive reactance (XC) = 20Ω.
Step 2: Write down the formula for total impedance in a series RLC circuit: Z = √(R² + (XL - XC)²).
Step 3: Substitute the known values into the formula: 50 = √(30² + (XL - 20)²).
Step 4: Calculate 30², which is 900. So, we have: 50 = √(900 + (XL - 20)²).
Step 5: Square both sides to eliminate the square root: 50² = 900 + (XL - 20)², which gives us 2500 = 900 + (XL - 20)².
Step 6: Subtract 900 from both sides: 2500 - 900 = (XL - 20)², resulting in 1600 = (XL - 20)².
Step 7: Take the square root of both sides: √1600 = XL - 20, which gives us 40 = XL - 20.
Step 8: Add 20 to both sides to solve for XL: 40 + 20 = XL, resulting in XL = 60Ω.
