At what frequency does a network composed of a 500-picofarad capacitor and a 600-ohm resistor have an impedance of 100 ohms, /0 degrees?

At what frequency does a network composed of a 500-picofarad capacitor and a 600-ohm resistor have an impedance of 100 ohms, /0 degrees?

• A. 50 kHz
• B. 100 kHz
• C. 200 kHz
• D. 300 kHz

Answer: (B)

To determine the frequency at which a network comprising a 500-picofarad capacitor and a 600-ohm resistor has an impedance of 100 ohms at 0 degrees, we can use the formula for the impedance of an RC circuit. In a series RC circuit, the total impedance (Z) can be expressed as: \[ Z = R + jX \] where \( R \) is the resistance, and \( jX \) represents the reactance due to the capacitor. The capacitive reactance (X) can be calculated using the formula: \[ X_C = \frac{1}{2 \pi f C} \] where: - \( f \) is the frequency in hertz, - \( C \) is the capacitance in farads, - \( j \) represents the imaginary unit (though we're concerned with the magnitude for calculating impedance). In this case, we are given: - \( R = 600 \, \Omega \) - \( C = 500 \, \text{pF} = 500 \times 10^{-12} \, \text{F} \) The total impedance needs to be 100 ohms at an angle of 0 degrees,

To determine the frequency at which a network comprising a 500-picofarad capacitor and a 600-ohm resistor has an impedance of 100 ohms at 0 degrees, we can use the formula for the impedance of an RC circuit.

In a series RC circuit, the total impedance (Z) can be expressed as:

[ Z = R + jX ]

where ( R ) is the resistance, and ( jX ) represents the reactance due to the capacitor. The capacitive reactance (X) can be calculated using the formula:

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

where:

• ( f ) is the frequency in hertz,

• ( C ) is the capacitance in farads,

• ( j ) represents the imaginary unit (though we're concerned with the magnitude for calculating impedance).

In this case, we are given:

• ( R = 600 , \Omega )

• ( C = 500 , \text{pF} = 500 \times 10^{-12} , \text{F} )

The total impedance needs to be 100 ohms at an angle of 0 degrees,