A resistance of 50 Ω is connected in series with an inductive reactance of 70 Ω and a capacitive reactance of 20 Ω. What is the impedance of the circuit?

To determine the impedance of the circuit consisting of resistance, inductive reactance, and capacitive reactance, it's essential to combine these impedances correctly.

In a series circuit containing a resistor (R), inductive reactance (X_L), and capacitive reactance (X_C), the total impedance (Z) can be calculated using the formula:

[ Z = R + j(X_L - X_C) ]

Where:

• ( R ) is the resistance.

• ( X_L ) is the inductive reactance.

• ( X_C ) is the capacitive reactance.

• ( j ) is the imaginary unit.

From the question, we have:

• Resistance ( R = 50 , \Omega )

• Inductive reactance ( X_L = 70 , \Omega )

• Capacitive reactance ( X_C = 20 , \Omega )

Now we can calculate the total reactance:

[ X_{total} = X_L - X_C = 70 , \Omega - 20 , \Omega = 50 , \Omega ]

This leads to the impedance being expressed as:

[ Z = 50 , \Omega + j50