https://file.aiquickdraw.com/mathbot/file/172731821698828h1mkz2.jpg

The circuit in the image shows resistors connected in both series and parallel, with the goal to find the total resistance (\(R_T\)).

### Resistors in the Circuit:
- \( R_1 = 50.092 \, \Omega \)
- \( R_2 = 1.072 \, \text{k}\Omega = 1072 \, \Omega \)
- \( R_3 = 560 \, \Omega \)
- \( R_4 = 25 \, \Omega \)
- \( R_5 = 13 \, \Omega \)

### Steps to solve for total resistance:
1. **Combine the resistances in series**:
   Resistors \( R_4 \) and \( R_5 \) are in series, so:
   \[
   R_{\text{45}} = R_4 + R_5 = 25 \, \Omega + 13 \, \Omega = 38 \, \Omega
   \]

2. **Combine resistances in parallel**:
   \( R_3 \) and \( R_{\text{45}} \) are in parallel. The formula for two resistors in parallel is:
   \[
   \frac{1}{R_{\text{345}}} = \frac{1}{R_3} + \frac{1}{R_{\text{45}}}
   \]
   Substituting values:
   \[
   \frac{1}{R_{\text{345}}} = \frac{1}{560 \, \Omega} + \frac{1}{38 \, \Omega}
   \]
   Calculating this will give \( R_{\text{345}} \).

3. **Combine the remaining series resistances**:
   The resistors \( R_1 \), \( R_2 \), and \( R_{\text{345}} \) are in series. The total resistance will be:
   \[
   R_T = R_1 + R_2 + R_{\text{345}}
   \]

I'll calculate the exact total resistance next.The total resistance \( R_T \) of the circuit is approximately \( 1157.68 \, \Omega \).

Would you like a more detailed explanation of any step, or do you have any additional questions?

Here are 5 related questions to expand your understanding:
1. How do you calculate the equivalent resistance for more than two resistors in parallel?
2. What effect does a parallel resistor have on the total resistance?
3. How would the total resistance change if you replaced \( R_1 \) with a larger resistor?
4. Can you derive the formula for resistors in parallel from Ohm’s law?
5. How can you use the total resistance to calculate current in the circuit if the voltage is known?

**Tip**: When dealing with resistors in parallel, the total resistance is always less than the smallest individual resistance in the parallel group.

Find the total resistance (RT) of the circuit with the following resistors: R1 = 50.092 Ω, R2 = 1.072 kΩ, R3 = 560 Ω, R4 = 25 Ω, R5 = 13 Ω. The circuit is powered by a 40V source.

Learn how to calculate the total resistance for a circuit with resistors in both series and parallel configurations. This example uses Ohm's law and covers the concepts of equivalent resistance. Suitable for Grades 10-12 physics students.

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