Write the phasor impedance for resistor, inductor, and capacitor, and give X_L and X_C.

Write the phasor impedance for resistor, inductor, and capacitor, and give X_L and X_C.

• A. Z_R = R; Z_L = j ω L; Z_C = -j /(ω C); X_L = ω L; X_C = ω C
• B. Z_R = R; Z_L = j ω L; Z_C = -j /(ω C); X_L = ω L; X_C = 1 /(ω C)
• C. Z_R = R; Z_L = -j ω L; Z_C = j /(ω C); X_L = -ω L; X_C = 1 /(ω C)
• D. Z_R = R; Z_L = j ω L; Z_C = -j /(ω C); X_L = 1 /(ω L); X_C = ω C

Answer: (B)

In phasor form, each element has an impedance that combines a real part (resistance) and an imaginary part (reac­tance). For the basic components the standard forms are: - Resistor: Z_R = R (purely real) - Inductor: Z_L = j ω L (positive imaginary) - Capacitor: Z_C = 1/(j ω C) = -j/(ω C) (negative imaginary) The reactances, which are the magnitudes of the imaginary parts, are defined as X_L = ω L and X_C = 1/(ω C). The signs sit in the impedance expressions above, with the inductor contributing +jωL and the capacitor contributing -j/(ωC). The option that matches these relationships is the one listing Z_R = R, Z_L = j ω L, Z_C = -j/(ω C) and X_L = ω L, X_C = 1/(ω C). The other options misstate either the imaginary signs or the X_L / X_C magnitudes.

In phasor form, each element has an impedance that combines a real part (resistance) and an imaginary part (reac­tance). For the basic components the standard forms are:

• Resistor: Z_R = R (purely real)

• Inductor: Z_L = j ω L (positive imaginary)

• Capacitor: Z_C = 1/(j ω C) = -j/(ω C) (negative imaginary)

The reactances, which are the magnitudes of the imaginary parts, are defined as X_L = ω L and X_C = 1/(ω C). The signs sit in the impedance expressions above, with the inductor contributing +jωL and the capacitor contributing -j/(ωC).

The option that matches these relationships is the one listing Z_R = R, Z_L = j ω L, Z_C = -j/(ω C) and X_L = ω L, X_C = 1/(ω C). The other options misstate either the imaginary signs or the X_L / X_C magnitudes.