In an RLC series circuit, if the total impedance is 20Ω and the resistance is 15Ω, what is the inductive reactance? (2022)

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Q: In an RLC series circuit, if the total impedance is 20Ω and the resistance is 15Ω, what is the inductive reactance? (2022)

Solution: Using Z = √(R² + (XL)²), solve for XL.

Steps: 10

Step 1: Identify the given values. The total impedance (Z) is 20Ω and the resistance (R) is 15Ω.
Step 2: Write down the formula for total impedance in an RLC series circuit: Z = √(R² + (XL)²).
Step 3: Substitute the known values into the formula: 20 = √(15² + (XL)²).
Step 4: Calculate 15², which is 225. Now the equation is: 20 = √(225 + (XL)²).
Step 5: Square both sides of the equation to eliminate the square root: 20² = 225 + (XL)².
Step 6: Calculate 20², which is 400. Now the equation is: 400 = 225 + (XL)².
Step 7: Subtract 225 from both sides to isolate (XL)²: 400 - 225 = (XL)².
Step 8: Calculate 400 - 225, which is 175. Now the equation is: 175 = (XL)².
Step 9: Take the square root of both sides to find XL: XL = √175.
Step 10: Calculate the square root of 175, which is approximately 13.23Ω.