Question

Find the simplest equivalent circuit (component values) that could be in a "black-box" with the following parameters : E = 120V∠0°, I = 6A∠30°, f = 60 Hz.

Answer 1

The simplest equivalent circuit in a 'black-box' with the parameters given can be deduced using AC circuit principles and phasor algebra to find impedance and component values for an RLC circuit.

Step-by-step explanation:

To determine the simplest equivalent circuit inside a 'black-box' with the given parameters, we need to use the concepts of AC circuits and phasor algebra to compute the impedance and component values. Given the parameters are: Voltage E = 120V∠0°, Current I = 6A∠30°, and frequency f = 60 Hz, we can find the impedance of the circuit.

To find the impedance Z, we use the formula Z = E / I, where E is the RMS voltage and I is the RMS current. First, we convert the phasor current to rectangular form using the phase angle given.

The rectangular form of current I is I = I0cos(θ) + j*I0sin(θ). Thus, I = 6(cos 30° + j*sin 30°) A = 6(0.866 + j*0.5) A = 5.196 + j*3 A. Now, the impedance Z = 120V / (5.196 + j*3) A. After calculation, we find the values of the resistance R and reactance X that represent the black-box circuit components.

The calculated values of R and X provide the component values for a series RLC circuit, which could consist of a resistor (R), an inductor (L), and a capacitor (C). By further analyzing the sign and magnitude of the reactance, it is possible to identify the dominance of either inductive or capacitive behavior.

Answer 2

In this case, the simplest equivalent circuit that could be in the "black-box" is a resistor with a value of 20 ohms.

Step-by-step explanation:

The "black-box" circuit is a way of representing an unknown circuit by providing its input and output parameters. In this case, the input parameters are E = 120V∠0° (voltage magnitude and phase angle) and I = 6A∠30° (current magnitude and phase angle), with a frequency of f = 60 Hz.

To find the simplest equivalent circuit, we can use Ohm's Law and the impedance concept. Ohm's Law states that the voltage across a component is equal to the product of its impedance and the current flowing through it.

Let's start by finding the impedance of the circuit. Impedance (Z) is a complex quantity that combines the resistance (R) and reactance (X) of a component.

The formula to calculate impedance in an AC circuit is Z = R + jX, where j represents the imaginary unit (√-1).

To find the resistance, we can use Ohm's Law. Resistance (R) is given by the formula R = V / I, where V is the voltage across the component and I is the current flowing through it.

In this case, the voltage (V) is 120V∠0° and the current (I) is 6A∠30°.

Using the formula R = V / I, we can calculate the resistance. Since the phase angle is 0° for the voltage, there is no reactance (X) present.

Therefore, the impedance (Z) of the circuit is equal to the resistance (R) only.

Now, let's calculate the resistance:

R = V / I = 120V / 6A = 20 ohms.

So, the impedance (Z) of the circuit is 20 ohms.

To summarize, the simplest equivalent circuit that could be in the "black-box" is a resistor with a value of 20 ohms.