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No circuito da Figura abaixo,  o fasor que representa a tensão da fonte é

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

The given circuit consists of an AC voltage source, a resistor, and an inductor. From the circuit diagram:

- The resistor has a value of \( 20\sqrt{3} \, \Omega \),
- The inductor is represented by a reactance \( j20 \, \Omega \),
- The current \( I_t \) and voltage \( V_t \) are represented in phasor form.

To determine the phasor for the current \( \hat{I} \), we can use **Ohm's Law for AC circuits**:
\[
\hat{I} = \frac{\hat{V}}{Z}
\]
where:
- \( \hat{V} \) is the phasor voltage from the source,
- \( Z \) is the total impedance of the circuit.

### Step 1: Calculate the total impedance \( Z \)
The total impedance \( Z \) is the sum of the resistive and inductive reactances:
\[
Z = R + jX_L
\]
where:
- \( R = 20\sqrt{3} \, \Omega \) (resistance),
- \( X_L = 20 \, \Omega \) (inductive reactance).

Thus, the total impedance is:
\[
Z = 20\sqrt{3} + j20
\]

### Step 2: Calculate the magnitude and phase of the impedance
To find the magnitude \( |Z| \) and phase \( \theta_Z \) of the impedance, we use the following formulas:

\[
|Z| = \sqrt{R^2 + X_L^2}
\]
and
\[
\theta_Z = \tan^{-1}\left(\frac{X_L}{R}\right)
\]

Let me calculate these values for you.The total impedance \( Z \) has a magnitude of 40 ohms and a phase angle of 30°.

### Step 3: Phasor current calculation
Now, the phasor current \( \hat{I} \) can be expressed as:
\[
\hat{I} = \frac{\hat{V}}{Z}
\]
If the voltage \( \hat{V} \) is given as \( V_t \), you can divide the phasor voltage by the magnitude and phase of the impedance to find the phasor current \( \hat{I} \).

Would you like me to proceed with calculating \( \hat{I} \) assuming a certain voltage, or do you have the value of \( \hat{V} \) available for the source? Let me know if you have any questions!

Here are some questions you can think about:
1. How do you determine the phase angle of the current relative to the voltage?
2. How does the inductive reactance affect the total impedance?
3. What would happen if the circuit had a capacitive reactance instead of an inductive one?
4. How would the current change if the resistor's value increased?
5. What are the real and reactive power components in this AC circuit?

**Tip:** In AC circuits, the impedance angle reflects the phase difference between voltage and current due to reactive components.

Learn how to calculate the phasor current in an AC circuit containing a resistor and an inductor. This problem involves determining the impedance, using Ohm's Law for AC circuits, and calculating the phasor current based on given voltage values. Explore the phase angle between current and voltage, the impact of inductive reactance on impedance, and more.

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