Question

A 40 µF capacitor is in series with a coil of resistance 8 ohms and inductance 80 mH is connected to a 200V, 100Hz supply. The ˚uit impedance can be calculated using:

a. Z= √(R^2 +(XL - XC)^2)
b. Z=R+XL+XC
c. Z-R/(XL - XC)
d. none of the above

Answer 1

The impedance of the RLC series circuit in question is calculated using the formula Z= √(R^2 +(XL - XC)^2). The resistance, inductive reactance (XL), and capacitive reactance (XC) must be computed with provided frequency, resistances, inductance, and capacitance values.

Step-by-step explanation:

The impedance of a series RLC circuit is given by the formula Z= √(R^2 +(XL - XC)^2), where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance. Inductive reactance is calculated using XL = 2πfL and capacitive reactance using XC = 1 / (2πfC). Given a coil with resistance 8 ohms and inductance of 80 mH in series with a 40 µF capacitor connected to a 200V, 100Hz supply, we calculate XL as XL = 2π(100)(0.08) and XC as XC = 1 / (2π(100)(40 × 10^{-6})). The correct formula to calculate the circuit impedance is option a: Z= √(R^2 +(XL - XC)^2).