Question

Determine the resistance and series inductance or capacitance for each of the following impedances assuming frequency of 50 hertz

4 + j7 ohms​

Answer 1

To determine the resistance and series inductance or capacitance for the impedance 4 + j7 ohms at a frequency of 50 Hz, we need to use the impedance formula for an RLC circuit:

Z = R + jX

where Z is the impedance, R is the resistance, and X is the reactance. The reactance can be inductive (X_L) or capacitive (X_C), depending on the component in the circuit.

For the given impedance of 4 + j7 ohms, we can see that the real part (4 ohms) represents the resistance and the imaginary part (7 ohms) represents the reactance. To determine whether the reactance is inductive or capacitive, we need to look at the sign of the imaginary part:

If the imaginary part is positive (as in this case), the reactance is inductive (X_L).
If the imaginary part is negative, the reactance is capacitive (X_C).
Therefore, for the given impedance:

Resistance = 4 ohms
Series inductance = X_L = 7 ohms
Note that we didn't need to use the frequency information to determine the resistance and inductance, as they are purely real and imaginary components respectively. However, the frequency would be needed to determine the actual value of the inductance or capacitance component in the circuit

Answer 2

Explanation:

To determine the resistance and series inductance or capacitance for the impedance 4+j7 ohms at a frequency of 50 Hz, we can use the following equations:

Resistance (R) = Re(Z)

Series Inductance (L) = Im(Z) / (2πf)

Series Capacitance (C) = -1 / (2πfIm(Z))

where Z is the complex impedance and f is the frequency.

Given the impedance is 4+j7 ohms at 50 Hz, we have:

Resistance (R) = 4 ohms

Series Inductance (L) = Im(Z) / (2πf) = 7 / (2π×50) ≈ 0.022 Henrys

Series Capacitance (C) = -1 / (2πfIm(Z)) = -1 / (2π×50×7) ≈ -0.0018 Farads

Note that the negative sign in the formula for series capacitance arises because the imaginary part of the impedance is positive, indicating a net inductive behavior. This means that to counteract the inductive behavior and achieve a purely resistive impedance, a capacitance must be added in series.