What is the rectangular coordinate impedance of a network consisting of a 10-microhenry inductor and a 20-ohm resistor at 1 MHz?

What is the rectangular coordinate impedance of a network consisting of a 10-microhenry inductor and a 20-ohm resistor at 1 MHz?

• A. 20 + j6.28
• B. 20 + j10
• C. 20 + j31.4
• D. 20 + j15.7

Answer: (C)

To determine the rectangular coordinate impedance of the network composed of an inductor and a resistor, we need to calculate the impedance of the inductor and then combine it with the resistance. The impedance of a resistor is purely real, represented by its resistance value, which in this case is 20 ohms. For the inductor, its impedance is given by the formula: \[ Z_L = j \omega L \] Where: - \( j \) is the imaginary unit. - \( \omega \) is the angular frequency, calculated as \( \omega = 2\pi f \), where \( f \) is the frequency in hertz. - \( L \) is the inductance in henries. Given that the frequency is 1 MHz, we can calculate \( \omega \): \[ \omega = 2 \pi (1 \times 10^6) \approx 6.2832 \times 10^6 \text{ radians/second} \] Now, we need to convert the inductance from microhenries to henries: \[ L = 10 \text{ microhenries} = 10 \times 10^{-6} \text{ henries} = 10

To determine the rectangular coordinate impedance of the network composed of an inductor and a resistor, we need to calculate the impedance of the inductor and then combine it with the resistance.

The impedance of a resistor is purely real, represented by its resistance value, which in this case is 20 ohms.

For the inductor, its impedance is given by the formula:

[ Z_L = j \omega L ]

Where:

• ( j ) is the imaginary unit.

• ( \omega ) is the angular frequency, calculated as ( \omega = 2\pi f ), where ( f ) is the frequency in hertz.

• ( L ) is the inductance in henries.

Given that the frequency is 1 MHz, we can calculate ( \omega ):

[ \omega = 2 \pi (1 \times 10^6) \approx 6.2832 \times 10^6 \text{ radians/second} ]

Now, we need to convert the inductance from microhenries to henries:

[ L = 10 \text{ microhenries} = 10 \times 10^{-6} \text{ henries} = 10