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

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

1. **Identify the Phasors**: We have the following phasors:
   - $$ V_L = 232.51 \angle 39^\circ \, 	ext{V} $$ (Voltage across the inductor)
   - $$ V_C = 165 \angle -142^\circ \, 	ext{V} $$ (Voltage across the capacitor)
   - $$ V_R = 62 \angle -52^\circ \, 	ext{V} $$ (Voltage across the resistor)
   - $$ I_T = 5.2 \angle -52^\circ \, 	ext{A} $$ (Total current)
   - $$ V_T = 200 \angle 10^\circ \, 	ext{V} $$ (Total voltage)

2. **Draw the Axes**: Start by drawing a horizontal line (real axis) and a vertical line (imaginary axis) to represent the complex plane.

3. **Plot the Phasors**:
   - **Voltage across the Resistor $$ V_R $$**: This phasor is at an angle of $$-52^\circ$$ from the positive real axis. 
   - **Voltage across the Inductor $$ V_L $$**: This phasor is at an angle of $$39^\circ$$ from the positive real axis.
   - **Voltage across the Capacitor $$ V_C $$**: This phasor is at an angle of $$-142^\circ$$ from the positive real axis.
   - **Total Current $$ I_T $$**: This phasor is at an angle of $$-52^\circ$$ from the positive real axis, which is the same as $$ V_R $$.
   - **Total Voltage $$ V_T $$**: This phasor is at an angle of $$10^\circ$$ from the positive real axis.

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

5. **Draw the Phasor Diagram**: Connect the phasors appropriately to show their relationships.

Now, let's summarize the angles and magnitudes for clarity:
- $$ V_R = 62 \angle -52^\circ $$
- $$ V_L = 232.51 \angle 39^\circ $$
- $$ V_C = 165 \angle -142^\circ $$
- $$ I_T = 5.2 \angle -52^\circ $$
- $$ V_T = 200 \angle 10^\circ $$

### Phasor Diagram

1. **Draw the horizontal axis (real axis)**.
2. **Draw the vertical axis (imaginary axis)**.
3. **Plot $$ V_R $$** at $$-52^\circ$$ with a length of 62.
4. **Plot $$ V_L $$** at $$39^\circ$$ with a length of 232.51.
5. **Plot $$ V_C $$** at $$-142^\circ$$ with a length of 165.
6. **Plot $$ I_T $$** at $$-52^\circ$$ with a length of 5.2.
7. **Plot $$ V_T $$** at $$10^\circ$$ with a length of 200.

### Final Note
To create a neat phasor diagram, you can use graphing software or draw it by hand, ensuring that the angles and lengths are accurately represented. Each phasor should be clearly labeled with its corresponding value and angle.
To draw the phasor diagram for the RLC circuit: 1. **Draw the Axes**: Create a horizontal (real) and vertical (imaginary) axis. 2. **Plot Each Phasor**: - $$ V_R = 62 \angle -52^\circ $$ - $$ V_L = 232.51 \angle 39^\circ $$ - $$ V_C = 165 \angle -142^\circ $$ - $$ I_T = 5.2 \angle -52^\circ $$ - $$ V_T = 200 \angle 10^\circ $$ 3. **Label Each Phasor** with its value and angle. 4. **Connect the Phasors** appropriately to show their relationships. Ensure the diagram is neat and accurately represents the angles and magnitudes of each phasor.

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