https://file.aiquickdraw.com/mathbot/file/1726199807663vw5ridwg.jpg

To find the total resistance \( R_{\text{total}} \) in this circuit, we need to break down the resistors into series and parallel combinations. Let’s work through it step by step based on the image provided:

### Resistor Breakdown:
1. The top branch consists of the resistors \( 3 \, \Omega \), \( 6 \, \Omega \), and \( 2 \, \Omega \) in series.
   - **Series Rule**: Resistors in series add directly.
   - So, the total resistance of the top branch is:
   \[
   R_{\text{top}} = 3 \, \Omega + 6 \, \Omega + 2 \, \Omega = 11 \, \Omega
   \]

2. The bottom branch consists of the resistors \( 4 \, \Omega \), \( 12 \, \Omega \), and \( 10 \, \Omega \), where \( 4 \, \Omega \) and \( 12 \, \Omega \) are in series and their combination is in parallel with the \( 10 \, \Omega \) resistor.
   - First, combine \( 4 \, \Omega \) and \( 12 \, \Omega \) (series):
   \[
   R_{\text{bottom-series}} = 4 \, \Omega + 12 \, \Omega = 16 \, \Omega
   \]
   - Now, combine \( 16 \, \Omega \) and \( 10 \, \Omega \) in parallel:
   \[
   \frac{1}{R_{\text{bottom}}} = \frac{1}{16 \, \Omega} + \frac{1}{10 \, \Omega}
   \]
   Let's calculate this explicitly.

I'll now calculate the total resistance step by step.The total resistance of the bottom branch, after combining \( 4 \, \Omega \), \( 12 \, \Omega \), and \( 10 \, \Omega \), is approximately \( 6.15 \, \Omega \).

### Next Steps:
Now, we have two resistances:


What is the total resistance (R_total) in the given circuit?

Learn how to calculate the total resistance (R_total) in a circuit involving series and parallel resistors. This step-by-step guide explains the process of combining resistors and applying Ohm's Law, suitable for high school students.

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