https://file.aiquickdraw.com/mathbot/file/1727754660417stk79vlx.jpg

To solve this, we need to find the equivalent capacitance between points A and B for the given group of capacitors. Here's the strategy:

1. **Capacitor configuration**: The circuit shows \( C_1 \) in series with the combination of \( C_2 \) and \( C_3 \), which are in parallel.

2. **Capacitance in parallel**: Capacitors \( C_2 \) and \( C_3 \) are in parallel, so their combined capacitance is the sum:
   \[
   C_{\text{parallel}} = C_2 + C_3 = 9.0 \, \mu F + 20 \, \mu F = 29.0 \, \mu F
   \]

3. **Capacitance in series**: Now, \( C_1 \) is in series with this parallel combination. For series capacitors, the formula is:
   \[
   \frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_{\text{parallel}}}
   \]
   Substituting the values:
   \[
   \frac{1}{C_{\text{eq}}} = \frac{1}{12 \, \mu F} + \frac{1}{29 \, \mu F}
   \]

4. **Calculating** \( C_{\text{eq}} \):
   \[
   \frac{1}{C_{\text{eq}}} = 0.0833 + 0.03448 = 0.11778
   \]
   \[
   C_{\text{eq}} = \frac{1}{0.11778} = 8.49 \, \mu F
   \]

Thus, the equivalent capacitance is approximately **8.5 µF** to two significant figures.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you calculate the total capacitance in a series circuit?
2. What happens to the overall capacitance when capacitors are connected in parallel?
3. How does increasing the capacitance of one component affect the total capacitance in a series circuit?
4. What are practical examples of series and parallel capacitors in electronics?
5. How would the equivalent capacitance change if \( C_1 \) were much larger?

**Tip**: In a series circuit, the total capacitance is always less than the smallest individual capacitor's value.

Find the equivalent capacitance between points A and B for the group of capacitors shown in the image. Suppose C1 = 12 µF, C2 = 9.0 µF, and C3 = 20 µF.

Learn how to calculate the equivalent capacitance between points A and B in a circuit containing three capacitors, C1 = 12 µF, C2 = 9.0 µF, and C3 = 20 µF, with a combination of series and parallel connections. This problem covers important concepts of capacitance in series and parallel circuits. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation