In polar coordinates, what is the impedance of a network composed of a 100-ohm-reactance inductor in series with a 100-ohm resistor?

In polar coordinates, what is the impedance of a network composed of a 100-ohm-reactance inductor in series with a 100-ohm resistor?

• A. 141 ohms, /45 degrees
• B. 100 ohms, /90 degrees
• C. 200 ohms, /45 degrees
• D. 141 ohms, /30 degrees

Answer: (A)

To solve for the impedance of a network composed of a 100-ohm resistive and a 100-ohm reactive component, you can use the principles of complex impedance. In polar coordinates, impedance is represented as a magnitude and phase angle. The resistance (100 ohms) and reactance (100 ohms for an inductor) can be combined to find the total impedance. The resistance contributes a real part, while the reactance contributes an imaginary part. In this case, since the inductor's reactance can be represented as +j100 ohms, the total impedance (Z) can be expressed as: Z = R + jX = 100 + j100. To convert this rectangular form to polar form, you first calculate the magnitude and phase angle: 1. **Magnitude (|Z|)**: \[ |Z| = \sqrt{R^2 + X^2} = \sqrt{100^2 + 100^2} = \sqrt{20000} = 141.42 \text{ ohms} \approx 141 \text{ ohms} \] 2. **Phase angle (θ)**: \[ \theta = \tan

To solve for the impedance of a network composed of a 100-ohm resistive and a 100-ohm reactive component, you can use the principles of complex impedance.

In polar coordinates, impedance is represented as a magnitude and phase angle. The resistance (100 ohms) and reactance (100 ohms for an inductor) can be combined to find the total impedance.

The resistance contributes a real part, while the reactance contributes an imaginary part. In this case, since the inductor's reactance can be represented as +j100 ohms, the total impedance (Z) can be expressed as:

Z = R + jX = 100 + j100.

To convert this rectangular form to polar form, you first calculate the magnitude and phase angle:

1. Magnitude (|Z|):

[

|Z| = \sqrt{R^2 + X^2} = \sqrt{100^2 + 100^2} = \sqrt{20000} = 141.42 \text{ ohms} \approx 141 \text{ ohms}

]

2. Phase angle (θ):

[

\theta = \tan