Question

A 40 mF capacitor in series with a coil of resistance 8 ohms and inductance 80 mH is connected to a 200V, 100Hz supply. Calculate the circuit impedance:

a. Z = √(R² + (X_L - X_C)²)
b. Z = √(R² + (X_L + X_C)²)
c. Z = √(R² + (X_L * X_C)²)
d. Z = √(R² + (X_L / X_C)²)

Answer 1

The impedance of a series RLC circuit is found using the formula Z = √(R² + (XL - XC)²). By calculating the inductive reactance (XL) and the capacitive reactance (XC), and given a resistance (R), we obtain the impedance (Z), which for the given values is 13.14 Ω. The correct option is 'a'.

Step-by-step explanation:

To calculate the impedance (Z) of a series RLC circuit given the resistance (R), inductance (L), and capacitance (C), we need to determine the inductive reactance (XL) and the capacitive reactance (XC), and then apply the correct formula.

The inductive reactance is given by XL = 2πfL, where f is the frequency of the supply and L is the inductance. The capacitive reactance is given by XC = 1 / (2πfC), where C is the capacitance.

For the given problem:

• Inductive reactance (XL) = 2π × 100 Hz × 80 mH = 50.27 Ω
• Capacitive reactance (XC) = 1 / (2π × 100 Hz × 40 mF) = 39.79 Ω

Then, the impedance of the circuit is calculated using the formula:

Z = √(R² + (XL - XC)²)

Which simplifies to:

Z = √(8Ω² + (50.27 Ω - 39.79 Ω)²) = √(8Ω² + 10.48Ω²)

Z = 13.14 Ω

The correct option for the given circuit impedance formula is: a. Z = √(R² + (XL - XC)²)