What is the impedance of a circuit with a 50 Ohm resistor in series and a capacitive reactance calculated as 30 Ohm?

To find the impedance of a circuit that consists of a resistor and capacitive reactance in series, you can apply the formula for total impedance, which combines both the resistance (R) and the reactance (X).

In this case, you have a resistor with a value of 50 Ohms and a capacitive reactance of 30 Ohms. When calculating impedance in a series circuit that includes a resistor and capacitive elements, you can use the following relationship:

Impedance (Z) is given by the formula:

[ Z = \sqrt{R^2 + (-X)^2} ]

Here, R is the resistance, and X is the capacitive reactance. Note that the capacitive reactance is considered as negative when adding to the impedance, but since we are taking the square in the formula, we can ignore the sign.

Plugging the values into the equation:

[ Z = \sqrt{50^2 + 30^2} ]

[ Z = \sqrt{2500 + 900} ]

[ Z = \sqrt{3400} ]

[ Z \approx 58.3 , \text{Ohm} ]

This calculation indicates that the total impedance