If a series circuit contains a pure inductance with a reactance of 200 ohms, a resistor of 1 k ohm, and a capacitor with a reactance of 250 ohms, what is the total impedance?

To determine the total impedance in a series circuit that includes a resistor, inductor, and capacitor, one must consider how to combine the resistive and reactive components effectively.

In this circuit, you have a resistor, a pure inductor, and a capacitor. The impedance of the resistor is simply its resistance, while the inductive and capacitive reactances need to be treated as imaginary components in terms of their effects on the total impedance.

The inductive reactance contributes positively to the total impedance (+j200 ohms), while the capacitive reactance contributes negatively (-j250 ohms). To find the net reactive impedance, you take the inductive reactance and subtract the capacitive reactance:

200 ohms (inductive) - 250 ohms (capacitive) = -50 ohms (net reactance).

This negative value indicates a net capacitive reactance in the circuit. The total impedance (Z) can then be expressed as a combination of the resistance (R) and the net reactance (X):

Z = R + jX,

Z = 1000 ohms + j(-50) ohms.

Now, to find the magnitude of the total impedance, we use the formula:

|Z