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

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