What is the resulting impedance when a 40-ohm resistor is added in series to the circuit?

When a resistor is added in series to a circuit, the total impedance (Z) is simply the sum of the individual resistances in the circuit. If you already have an original impedance, let's say it’s 10 ohms, and you add a 40-ohm resistor in series, the calculation would be straightforward.

For example:

Original impedance = 10 ohms

Added impedance = 40 ohms

The total impedance becomes:

Z = 10 ohms + 40 ohms = 50 ohms

If the original impedance you are adding the 40-ohm resistor to was, for example, 10 ohms, doubling this with the series addition yields an impedance of 50 ohms. Therefore, when selecting the answer, it is confirmed that the answer is a total of 50 ohms after adding a 40-ohm resistor in series to an existing impedance of 10 ohms.

This demonstrates how series circuits work concerning impedance: simply add up the resistances. The result being 50 ohms accurately reflects the equation and principles governing series circuits in electrical theory.