A series circuit has R = 4 Ω, XL = 3 Ω and Xc = 5 Ω at a given frequency. What is the impedance magnitude?

A series circuit has R = 4 Ω, XL = 3 Ω and Xc = 5 Ω at a given frequency. What is the impedance magnitude?

• A. About 6.0 Ω
• B. About 4.47 Ω
• C. About 4.0 Ω
• D. About 5.2 Ω

Answer: (B)

In a series circuit with a resistor and reactive elements, the impedance combines as Z = R + j(XL − Xc). The magnitude is |Z| = sqrt(R^2 + (XL − Xc)^2). Here XL − Xc = 3 − 5 = −2, so |Z| = sqrt(4^2 + (−2)^2) = sqrt(16 + 4) = sqrt(20) ≈ 4.47 Ω. The negative sign just indicates the net reactance is capacitive, but magnitude uses the square, so the result is about 4.47 Ω.

In a series circuit with a resistor and reactive elements, the impedance combines as Z = R + j(XL − Xc). The magnitude is |Z| = sqrt(R^2 + (XL − Xc)^2). Here XL − Xc = 3 − 5 = −2, so |Z| = sqrt(4^2 + (−2)^2) = sqrt(16 + 4) = sqrt(20) ≈ 4.47 Ω. The negative sign just indicates the net reactance is capacitive, but magnitude uses the square, so the result is about 4.47 Ω.