Continuing with the same setup as above, where you connect a 6Q resistor and a 12 Q resistor in parallel to a 9 V battery. Find the total equivalent current, ITot, flowing through the battery in Amperes. RTot ITot R1 R2 BAT1 12 Q 9 V

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---

### Basic Electrical Equations

- \( V = IR \)
- \( I = \frac{V}{R} \)
- \( R = \frac{V}{I} \)

### Series Circuits

- \( I_{\text{Tot}} = I_{1} = I_{2} \)
- \( V_{\text{Tot}} = V_{1} + V_{2} \)
- \( R_{\text{Tot}} = R_{1} + R_{2} \)

### Parallel Circuits

- \( I_{\text{Tot}} = I_{1} + I_{2} \)
- \( V_{\text{Tot}} = V_{1} = V_{2} \)
- \(\frac{1}{R_{\text{Tot}}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} \)
- \( R_{\text{Tot}} = \frac{R_{1} \cdot R_{2}}{R_{1} + R_{2}} \)

---

These equations summarize the fundamental principles of electrical circuits concerning Ohm's Law and the behavior of resistors in series and parallel configurations.
Transcribed Image Text:Here is the transcription of the provided image for educational purposes: --- ### Basic Electrical Equations - \( V = IR \) - \( I = \frac{V}{R} \) - \( R = \frac{V}{I} \) ### Series Circuits - \( I_{\text{Tot}} = I_{1} = I_{2} \) - \( V_{\text{Tot}} = V_{1} + V_{2} \) - \( R_{\text{Tot}} = R_{1} + R_{2} \) ### Parallel Circuits - \( I_{\text{Tot}} = I_{1} + I_{2} \) - \( V_{\text{Tot}} = V_{1} = V_{2} \) - \(\frac{1}{R_{\text{Tot}}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} \) - \( R_{\text{Tot}} = \frac{R_{1} \cdot R_{2}}{R_{1} + R_{2}} \) --- These equations summarize the fundamental principles of electrical circuits concerning Ohm's Law and the behavior of resistors in series and parallel configurations.
**Finding the Total Equivalent Current in a Parallel Resistive Circuit**

When two resistors are connected in parallel to a voltage source, the total equivalent resistance can be found using the formula:

\[ \frac{1}{R_{\text{Tot}}} = \frac{1}{R_1} + \frac{1}{R_2} \]

Given:
- Resistor \( R_1 = 6 \, \Omega \)
- Resistor \( R_2 = 12 \, \Omega \)
- Voltage of the battery \( V = 9 \, \text{V} \) (labeled as BAT1 in the diagram)

**Steps to find the total equivalent resistance \( R_{\text{Tot}} \):**

1. Calculate the reciprocal of each resistance:
\[ \frac{1}{R_1} = \frac{1}{6} \]
\[ \frac{1}{R_2} = \frac{1}{12} \]

2. Add these reciprocals together:
\[ \frac{1}{R_{\text{Tot}}} = \frac{1}{6} + \frac{1}{12} \]
\[ = \frac{2}{12} + \frac{1}{12} \]
\[ = \frac{3}{12} \]
\[ = \frac{1}{4} \]

3. Take the reciprocal of the result to find \( R_{\text{Tot}} \):
\[ R_{\text{Tot}} = 4 \, \Omega \]

**Now, to find the total current \( I_{\text{Tot}} \), use Ohm's Law:**

\[ I = \frac{V}{R} \]

So,
\[ I_{\text{Tot}} = \frac{9 \, \text{V}}{4 \, \Omega} \]
\[ I_{\text{Tot}} = 2.25 \, \text{A} \]

**Summary of Results:**

- The total equivalent resistance \( R_{\text{Tot}} \) is \( 4 \, \Omega \).
- The total current \( I_{\text{Tot}} \) flowing through the battery is \( 2.25 \, \text{A} \).

**Diagram Explanation:**

The provided circuit diagram illustrates the following components and their connections:

1. A voltage source labeled \( \text{BAT1} \), providing \(
Transcribed Image Text:**Finding the Total Equivalent Current in a Parallel Resistive Circuit** When two resistors are connected in parallel to a voltage source, the total equivalent resistance can be found using the formula: \[ \frac{1}{R_{\text{Tot}}} = \frac{1}{R_1} + \frac{1}{R_2} \] Given: - Resistor \( R_1 = 6 \, \Omega \) - Resistor \( R_2 = 12 \, \Omega \) - Voltage of the battery \( V = 9 \, \text{V} \) (labeled as BAT1 in the diagram) **Steps to find the total equivalent resistance \( R_{\text{Tot}} \):** 1. Calculate the reciprocal of each resistance: \[ \frac{1}{R_1} = \frac{1}{6} \] \[ \frac{1}{R_2} = \frac{1}{12} \] 2. Add these reciprocals together: \[ \frac{1}{R_{\text{Tot}}} = \frac{1}{6} + \frac{1}{12} \] \[ = \frac{2}{12} + \frac{1}{12} \] \[ = \frac{3}{12} \] \[ = \frac{1}{4} \] 3. Take the reciprocal of the result to find \( R_{\text{Tot}} \): \[ R_{\text{Tot}} = 4 \, \Omega \] **Now, to find the total current \( I_{\text{Tot}} \), use Ohm's Law:** \[ I = \frac{V}{R} \] So, \[ I_{\text{Tot}} = \frac{9 \, \text{V}}{4 \, \Omega} \] \[ I_{\text{Tot}} = 2.25 \, \text{A} \] **Summary of Results:** - The total equivalent resistance \( R_{\text{Tot}} \) is \( 4 \, \Omega \). - The total current \( I_{\text{Tot}} \) flowing through the battery is \( 2.25 \, \text{A} \). **Diagram Explanation:** The provided circuit diagram illustrates the following components and their connections: 1. A voltage source labeled \( \text{BAT1} \), providing \(
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