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?

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?

• A. 70.71 Ω
• B. 50 Ω
• C. 60 Ω
• D. 80 Ω

Answer: (A)

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

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