https://file.aiquickdraw.com/mathbot/file/17252936194673brsb24v.jpg

No circuito da Figura abaixo,  o fasor que representa a tensão da fonte é 120**∠**0v

O fasor que representa a corrente Î do circuito, dado em ampères, é:

The phasor that represents the voltage \( \hat{V_t} \) of the source is given as \( 120 \angle 0^\circ \) volts. We are now tasked with determining the phasor that represents the current \( \hat{I_t} \) in the circuit.

### Step 1: Recall the total impedance
From the previous calculation:
\[
Z = 20\sqrt{3} + j20 \, \Omega
\]
The magnitude and phase of the impedance were found to be:
\[
|Z| = 40 \, \Omega, \quad \theta_Z = 30^\circ
\]

### Step 2: Apply Ohm's Law for AC circuits
Using Ohm's Law in phasor form:
\[
\hat{I_t} = \frac{\hat{V_t}}{Z}
\]
where \( \hat{V_t} = 120 \angle 0^\circ \, V \).

Now, we'll calculate the current phasor using the voltage and impedance values.

Let me proceed with the calculation.# Given phasor voltage V_t = 120 ∠ 0° volts
V_t_magnitude = 120  # Magnitude of the voltage (in volts)
V_t_phase = 0  # Phase angle of the voltage (in degrees)

# Impedance magnitude and phase from the previous calculation
Z_magnitude = 40  # Magnitude of impedance (in ohms)
Z_phase = 30  # Phase angle of impedance (in degrees)

# Calculate the current magnitude and phase
I_t_magnitude = V_t_magnitude / Z_magnitude
I_t_phase = V_t_phase - Z_phase

I_t_magnitude, I_t_phaseThe phasor that represents the current \( \hat{I_t} \) in the circuit is:

\[
\hat{I_t} = 3 \angle -30^\circ \, \text{A}
\]

This means the current has a magnitude of 3 amperes and lags the voltage by 30 degrees, which is typical for an inductive circuit.

Let me know if you need any further clarifications!

Here are some additional questions to consider:
1. How would the phase angle change if the reactance of the inductor increased?
2. What is the power factor of this circuit?
3. How would the current change if the voltage were doubled?
4. What happens to the phase relationship between voltage and current in purely resistive circuits?
5. How does the reactance of the inductor change with frequency?

**Tip:** In AC circuits, current lags the voltage in inductive components, while it leads the voltage in capacitive components.

Learn how to calculate the current in an AC circuit given the voltage and impedance using phasor analysis. This problem involves applying Ohm's Law in phasor form and understanding the phase relationship between voltage and current. Suitable for advanced high school students or introductory college courses in electrical engineering.

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