In an RLC circuit, if the resistance is 10Ω, the inductance is 0.1H, and the cap

In an RLC circuit, if the resistance is 10Ω, the inductance is 0.1H, and the capacitance is 20μF, what is the total impedance at 50Hz? (2022)

In an RLC circuit, if the resistance is 10Ω, the inductance is 0.1H, and the capacitance is 20μF, what is the total impedance at 50Hz? (2022)

Step 1: Identify the given values: Resistance (R) = 10Ω, Inductance (L) = 0.1H, Capacitance (C) = 20μF, Frequency (f) = 50Hz.
Step 2: Convert capacitance from microfarads to farads: 20μF = 20 x 10^-6 F = 0.00002 F.
Step 3: Calculate the inductive reactance (XL) using the formula: XL = 2πfL.
Step 4: Substitute the values into the formula: XL = 2π(50)(0.1) = 31.42Ω.
Step 5: Calculate the capacitive reactance (XC) using the formula: XC = 1/(2πfC).
Step 6: Substitute the values into the formula: XC = 1/(2π(50)(0.00002)) = 159.15Ω.
Step 7: Calculate the total impedance (Z) using the formula: Z = √(R² + (XL - XC)²).
Step 8: Substitute the values into the formula: Z = √(10² + (31.42 - 159.15)²).
Step 9: Calculate the difference: XL - XC = 31.42 - 159.15 = -127.73.
Step 10: Square the difference: (-127.73)² = 16319.52.
Step 11: Calculate R²: 10² = 100.
Step 12: Add R² and the squared difference: 100 + 16319.52 = 16419.52.
Step 13: Take the square root to find Z: Z = √(16419.52) = 128.14Ω.

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