What is the impedance for a network composed of a 300-ohm-reactance capacitor, a 600-ohm-reactance inductor, and a 400-ohm resistor, all connected in series?

To determine the impedance of a series network comprising a resistor, capacitor, and inductor, we need to understand how impedance is calculated for each component and how they combine in the series configuration.

The impedance of a resistor is simply its resistance value, which in this case is 400 ohms. The capacitor provides a negative reactance, while the inductor provides a positive reactance. The reactance of the capacitor is -300 ohms, and the reactance of the inductor is +600 ohms.

In a series circuit, impedance is a complex value given by the formula:

Z = R + j(X_L - X_C),

where R is the resistance, X_L is the inductive reactance, and X_C is the capacitive reactance (expressed as a negative value).

Substituting in the values:

• Resistance (R) = 400 ohms

• Inductive reactance (X_L) = +600 ohms

• Capacitive reactance (X_C) = -300 ohms

Calculating the total reactance:

Total reactance = X_L - X_C = 600 ohms - 300 ohms = 300 ohms.

Now, substitute this back into the impedance