What is the impedance of a network composed of a 10-microhenry inductor in series with a 40-ohm resistor, at 500 MHz?

What is the impedance of a network composed of a 10-microhenry inductor in series with a 40-ohm resistor, at 500 MHz?

• A. 40 + j31400
• B. 30 + j31400
• C. 40 + j30000
• D. 40 + j3000

Answer: (A)

To find the impedance of a network that includes a series combination of a resistor and an inductor, we need to consider both the resistive and reactive components of the circuit. The impedance of a resistor is simply its resistance value, which, in this case, is 40 ohms. The impedance of an inductor is given by the formula \(Z_L = j\omega L\), where \(j\) is the imaginary unit, \(\omega\) is the angular frequency in radians per second, and \(L\) is the inductance in henries. First, we need to calculate the angular frequency \(\omega\): \[ \omega = 2\pi f \] Given that the frequency \(f\) is 500 MHz: \[ \omega = 2\pi \times 500 \times 10^6 \approx 3.14 \times 10^9 \text{ radians/second} \] Now, substituting in the values: \[ Z_L = j\omega L = j(3.14 \times 10^9)(10 \times 10^{-6}) = j(3.14 \times 10^3) = j314

To find the impedance of a network that includes a series combination of a resistor and an inductor, we need to consider both the resistive and reactive components of the circuit.

The impedance of a resistor is simply its resistance value, which, in this case, is 40 ohms. The impedance of an inductor is given by the formula (Z_L = j\omega L), where (j) is the imaginary unit, (\omega) is the angular frequency in radians per second, and (L) is the inductance in henries.

First, we need to calculate the angular frequency (\omega):

[

\omega = 2\pi f

]

Given that the frequency (f) is 500 MHz:

[

\omega = 2\pi \times 500 \times 10^6 \approx 3.14 \times 10^9 \text{ radians/second}

]

Now, substituting in the values:

[

Z_L = j\omega L = j(3.14 \times 10^9)(10 \times 10^{-6}) = j(3.14 \times 10^3) = j314