A resistance of 60 Ω is connected in series with an inductive reactance of 50 Ω and a capacitive reactance of 40 Ω. What is the impedance of the circuit?

To determine the impedance of a circuit that includes a resistance, inductive reactance, and capacitive reactance when connected in series, we can use the following formula for total impedance (Z):

Z = R + j(X_L - X_C)

Here, R is the resistance, X_L is the inductive reactance, X_C is the capacitive reactance, and j is the imaginary unit.

In this scenario, the resistance R is 60 Ω, the inductive reactance X_L is 50 Ω, and the capacitive reactance X_C is 40 Ω. It's important to note that in a series circuit, inductive reactance and capacitive reactance can be treated as positive and negative components, respectively. Thus, we calculate the net reactance (X) as follows:

X = X_L - X_C

X = 50 Ω - 40 Ω = 10 Ω (inductive, as it is positive)

Now, we can substitute the values for R and X into the impedance formula:

Z = 60 Ω + j(10 Ω)

To find the magnitude of the total impedance (|Z|), we use the formula for the magnitude of a complex number:

|Z| = √