In an RLC series circuit, if the total impedance is 20Ω and the resistance is 15

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

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

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.

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