What is the impedance expressed in polar coordinates of a series network consisting of a 200-ohm resistor and a 150-ohm-reactance inductor?

What is the impedance expressed in polar coordinates of a series network consisting of a 200-ohm resistor and a 150-ohm-reactance inductor?

• A. 250 ohms, /-36.9 degrees
• B. 200 ohms, /-36.9 degrees
• C. 250 ohms, /36.9 degrees
• D. 150 ohms, /36.9 degrees

Answer: (A)

To determine the impedance of a series network consisting of a resistor and an inductor, we need to combine the resistive and reactive components. The impedance \( Z \) of a circuit in polar form can be expressed as: \[ Z = R + jX \] where \( R \) is the resistance in ohms, \( j \) is the imaginary unit, and \( X \) is the reactance in ohms. In this case, we have: - A resistance \( R = 200 \, \Omega \) - An inductive reactance \( X = +150 \, \Omega \) To find the total impedance, we can use the following steps: 1. **Calculate the magnitude of the total impedance:** The magnitude \( |Z| \) is calculated using the Pythagorean theorem: \[ |Z| = \sqrt{R^2 + X^2} = \sqrt{(200)^2 + (150)^2} \] Calculating this gives: \[ |Z| = \sqrt{40000 + 22500} = \sqrt{62500} = 250 \, \Omega \] 2. **Calculate the phase angle

To determine the impedance of a series network consisting of a resistor and an inductor, we need to combine the resistive and reactive components.

The impedance ( Z ) of a circuit in polar form can be expressed as:

[

Z = R + jX

]

where ( R ) is the resistance in ohms, ( j ) is the imaginary unit, and ( X ) is the reactance in ohms.

In this case, we have:

• A resistance ( R = 200 , \Omega )

• An inductive reactance ( X = +150 , \Omega )

To find the total impedance, we can use the following steps:

1. Calculate the magnitude of the total impedance:

The magnitude ( |Z| ) is calculated using the Pythagorean theorem:

[

|Z| = \sqrt{R^2 + X^2} = \sqrt{(200)^2 + (150)^2}

]

Calculating this gives:

[

|Z| = \sqrt{40000 + 22500} = \sqrt{62500} = 250 , \Omega

]

2. **Calculate the phase angle