What is the impedance of a network with a 0.01-microfarad capacitor in parallel with a 300-ohm resistor, at 50 kHz?

What is the impedance of a network with a 0.01-microfarad capacitor in parallel with a 300-ohm resistor, at 50 kHz?

• A. 159 - j150
• B. 150 - j150
• C. 300 - j150
• D. 159 + j150

Answer: (A)

To find the impedance of a network that includes a 0.01-microfarad capacitor in parallel with a 300-ohm resistor at a frequency of 50 kHz, we first need to calculate the reactance of the capacitor and then combine it with the resistance. The reactance (X_C) of the capacitor can be calculated using the formula: \[ X_C = \frac{1}{2 \pi f C} \] Where: - \( f \) is the frequency (50,000 Hz) - \( C \) is the capacitance (0.01 microfarads or \( 0.01 \times 10^{-6} \) farads) Calculating the reactance: \[ X_C = \frac{1}{2 \pi (50000)(0.01 \times 10^{-6})} \] \[ X_C \approx \frac{1}{3.14 \times 0.0005} \approx \frac{1}{0.00157} \approx 636.62 \, \text{ohms} \] This reactance is negative because it represents a capacitive reactance, so we have: \[ X_C

To find the impedance of a network that includes a 0.01-microfarad capacitor in parallel with a 300-ohm resistor at a frequency of 50 kHz, we first need to calculate the reactance of the capacitor and then combine it with the resistance.

The reactance (X_C) of the capacitor can be calculated using the formula:

[

X_C = \frac{1}{2 \pi f C}

]

Where:

• ( f ) is the frequency (50,000 Hz)

• ( C ) is the capacitance (0.01 microfarads or ( 0.01 \times 10^{-6} ) farads)

Calculating the reactance:

[

X_C = \frac{1}{2 \pi (50000)(0.01 \times 10^{-6})}

]

[

X_C \approx \frac{1}{3.14 \times 0.0005} \approx \frac{1}{0.00157} \approx 636.62 , \text{ohms}

]

This reactance is negative because it represents a capacitive reactance, so we have:

[

X_C