In a series RLC circuit, the magnitude of the total impedance is given by which expression?

• A. |Z| = sqrt( R^2 + (ωL - 1/(ωC))^2 )
• B. |Z| = sqrt( R^2 - (ωL - 1/(ωC))^2 )
• C. |Z| = R^2 + (ωL - 1/(ωC))^2
• D. |Z| = R

Answer: (A)

In a series RLC circuit, the total impedance is a combination of resistance and the net reactive effect from the inductor and capacitor. The impedance can be written as Z = R + j(ωL − 1/(ωC)). The magnitude of this complex quantity is found by treating the real part and the imaginary part as perpendicular components, so the length is |Z| = sqrt(R^2 + (ωL − 1/(ωC))^2). This is the expression that accounts for both the resistive part and the net reactance.

The other forms would misrepresent the magnitude by omitting the square, subtracting the squares, or ignoring the reactive part altogether. Note that if ωL equals 1/(ωC), the net reactance is zero and the impedance reduces to |Z| = R.