Question

An RLC series circuit has R = 56 Ω, XL = 64 Ω, and XC = 37 Ω. What is the value of Z?

Answer 1

To calculate the impedance (Z) of an RLC series circuit with R = 56 Ω, XL = 64 Ω, and XC = 37 Ω, use the formula Z = √R² + (XL - XC)². After performing the calculations, the impedance Z is found to be approximately 62.17 Ω.

Step-by-step explanation:

The student is asking about the calculation of impedance (Z) in an RLC series circuit. The given values are R (resistance) = 56 Ω, XL (inductive reactance) = 64 Ω, and XC (capacitive reactance) = 37 Ω. To solve for impedance Z in such a circuit, the formula Z = √R² + (XL - XC)² is used.

In this case, the impedance Z can be calculated as follows:

1. Calculate the difference between the inductive and capacitive reactance: (XL - XC) = (64 Ω - 37 Ω) = 27 Ω.
2. Square the resistance: R² = (56 Ω)² = 3136 Ω².
3. Square the difference calculated in step 1: (XL - XC)² = (27 Ω)² = 729 Ω².
4. Add the squared resistance to the squared difference: R² + (XL - XC)² = 3136 Ω² + 729 Ω² = 3865 Ω².
5. Take the square root of the sum to find Z: Z = √3865 Ω² ≈ 62.17 Ω.

Therefore, the impedance Z of the RLC series circuit is approximately 62.17 Ω.