Activity 2.4 1. The following values were calculated from an $$ R L C $$ circuit. Draw a neat phasor diagram of this circuit with labels. $$ V_{L}=232,5139^{\circ} \mathrm{V} $$ $$ V_{C}=165-142^{\circ} \mathrm{V} $$ $$ V_{R}=62 \angle-52^{\circ} \mathrm{V} $$ $$ I_{\mathrm{T}}=5,2 \angle-52^{\circ} \mathrm{A} $$ $$ V_{\mathrm{T}}=20010^{\circ} \mathrm{V} $$

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To create a phasor diagram for the given $$ RLC $$ circuit, we will follow these steps:

1. **Identify the Phasors**: We have the following phasors:
   - $$ V_L = 232 \angle 5139^\circ \, \text{V} $$
   - $$ V_C = 165 \angle -142^\circ \, \text{V} $$
   - $$ V_R = 62 \angle -52^\circ \, \text{V} $$
   - $$ I_T = 5.2 \angle -52^\circ \, \text{A} $$
   - $$ V_T = 200 \angle 10^\circ \, \text{V} $$

2. **Convert Angles**: Since angles in phasors are typically represented within the range of $$ 0^\circ $$ to $$ 360^\circ $$, we will convert any angles that exceed this range.

- For $$ V_L $$:
     $$
     5139^\circ \mod 360 = 5139 - 14 \times 360 = 219^\circ
     $$
   - For $$ V_C $$, it is already in the correct range.
   - For $$ V_R $$, it is already in the correct range.
   - For $$ I_T $$, it is already in the correct range.
   - For $$ V_T $$, it is already in the correct range.

3. **Draw the Phasor Diagram**: The phasor diagram will represent the voltages and current as vectors in the complex plane.

- **Reference Axis**: We will use the horizontal axis (real axis) as the reference for $$ V_R $$ and $$ I_T $$ since they have the same angle.
   - **Positioning the Phasors**:
     - $$ V_R $$ will be drawn at an angle of $$ -52^\circ $$ from the horizontal axis.
     - $$ I_T $$ will also be drawn at an angle of $$ -52^\circ $$ from the horizontal axis.
     - $$ V_L $$ will be drawn at an angle of $$ 219^\circ $$.
     - $$ V_C $$ will be drawn at an angle of $$ -142^\circ $$.
     - $$ V_T $$ will be drawn at an angle of $$ 10^\circ $$.

4. **Label the Phasors**: Each phasor will be labeled with its corresponding voltage or current.

Now, let's create the phasor diagram.

### Phasor Diagram

- **$$ V_R $$**: Drawn at $$ -52^\circ $$ from the horizontal axis.
- **$$ I_T $$**: Drawn at $$ -52^\circ $$ from the horizontal axis, coinciding with $$ V_R $$.
- **$$ V_L $$**: Drawn at $$ 219^\circ $$ from the horizontal axis.
- **$$ V_C $$**: Drawn at $$ -142^\circ $$ from the horizontal axis.
- **$$ V_T $$**: Drawn at $$ 10^\circ $$ from the horizontal axis.

### Final Representation

The phasor diagram will visually represent the relationships between these voltages and the current in the circuit.

Since I cannot draw directly, I recommend using graphing software or a drawing tool to plot these vectors based on the angles and magnitudes provided. Each vector should be drawn from the origin, and the angles should be measured counterclockwise from the positive real axis.
To draw the phasor diagram for the $$ RLC $$ circuit: 1. **Identify Phasors**: - $$ V_L = 232 \angle 219^\circ \, \text{V} $$ - $$ V_C = 165 \angle -142^\circ \, \text{V} $$ - $$ V_R = 62 \angle -52^\circ \, \text{V} $$ - $$ I_T = 5.2 \angle -52^\circ \, \text{A} $$ - $$ V_T = 200 \angle 10^\circ \, \text{V} $$ 2. **Draw Vectors**: - Draw $$ V_R $$ and $$ I_T $$ at $$ -52^\circ $$. - Draw $$ V_L $$ at $$ 219^\circ $$. - Draw $$ V_C $$ at $$ -142^\circ $$. - Draw $$ V_T $$ at $$ 10^\circ $$. 3. **Label Each Vector** with its corresponding value. This diagram will show the relationships between the voltages and current in the circuit.

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