https://file.aiquickdraw.com/mathbot/file/1729866518074wgqlxvt0.jpg

Let's break down the circuit based on the diagram you provided and the questions.

### Circuit Analysis:
1. **Combination of Resistors**: 
   - The circuit has a parallel combination of three branches:
     - Branch 1: Contains a 12 Ω resistor.
     - Branch 2: Contains a 6 Ω resistor.
     - Branch 3: Contains a 9 Ω resistor in series with a 9 Ω resistor (total resistance for branch 3 is 9 + 9 = 18 Ω).
   
2. **Calculation of Total Resistance**:
   Since the three branches are in parallel, we use the formula for total resistance in parallel circuits:
   \[
   \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}
   \]
   Substituting the values for the branches:
   \[
   \frac{1}{R_{total}} = \frac{1}{12} + \frac{1}{6} + \frac{1}{18}
   \]
   Solving this:
   \[
   \frac{1}{R_{total}} = \frac{1}{12} + \frac{1}{6} + \frac{1}{18} = 0.0833 + 0.1667 + 0.0556 = 0.3056
   \]
   \[
   R_{total} = \frac{1}{0.3056} \approx 3.272 \, \Omega
   \]

3. **Calculation of Total Current**:
   Using Ohm's Law, \( I = \frac{V}{R} \), where \( V = 9 \, V \) and \( R_{total} = 3.272 \, \Omega \):
   \[
   I_{total} = \frac{9}{3.272} \approx 2.751 \, A
   \]

4. **Current in Each Branch**:
   Using Ohm's Law for each branch:
   - **First Branch (12 Ω)**: 
     \[
     I_1 = \frac{9}{12} = 0.750 \, A
     \]
   - **Second Branch (6 Ω)**: 
     \[
     I_2 = \frac{9}{6} = 1.500 \, A
     \]
   - **Third Branch (18 Ω)**: 
     \[
     I_3 = \frac{9}{18} = 0.500 \, A
     \]

### Summary of Answers:
1. **Total Resistance**: 3.272 Ω.
2. **Total Current**: 2.751 A.
3. **Current in First Branch**: 0.750 A.
4. **Current in Second Branch**: 1.500 A.

Would you like further details on any of these steps? Here are a few related questions you could explore:

1. How does the resistance change if the 12 Ω resistor is replaced by a 10 Ω resistor?
2. What happens to the total current if the voltage is increased to 12 V?
3. Can you explain the difference between series and parallel circuits?
4. How would the total resistance change if one of the branches is removed?
5. What would the current be if an additional resistor is added to the third branch?

**Tip**: In parallel circuits, the total resistance is always less than the smallest individual resistance in the branches.

Calculate total resistance, total current, and current in each branch based on the provided circuit diagram.

Learn how to calculate the total resistance and total current in a parallel circuit with three branches, using Ohm's Law and parallel resistance formulas. Understand how to find the current in each branch. Suitable for students in Grades 9-12.

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