**Capacitor System Analysis**For the system of capacitors shown in the figure below, find the following. (Let $ C_1 = 9.00 \, \mu\text{F} $ and $ C_2 = 7.00 \, \mu\text{F} $.)**Figure Explanation:**- The diagram shows a circuit with three capacitors.- $ C_1 = 9.00 \, \mu\text{F} $, $ C_2 = 7.00 \, \mu\text{F} $, and a third capacitor of $ 2.00 \, \mu\text{F} $.- These capacitors are connected across a $ 90.0 \, \text{V} $ battery.**Tasks:**(a) **Find the equivalent capacitance of the system:**- The equivalent capacitance is: $\_\_\_\_\_$ \, \mu\text{F}.(b) **Determine the charge on each capacitor:**- Charge on $ C_1 $: $\_\_\_\_\_$ \, \mu\text{C}.- Charge on $ C_2 $: $\_\_\_\_\_$ \, \mu\text{C}.- Charge on the $ 6.00 \, \mu\text{F} $ capacitor: $\_\_\_\_\_$ \, \mu\text{C}.- Charge on the $ 2.00 \, \mu\text{F} $ capacitor: $\_\_\_\_\_$ \, \mu\text{C}.(c) **Determine the potential difference across each capacitor:**- Potential difference across $ C_1 $: $\_\_\_\_\_$ \, V.- Potential difference across $ C_2 $: $\_\_\_\_\_$ \, V.- Potential difference across the $ 6.00 \, \mu\text{F} $ capacitor: $\_\_\_\_\_$ \, V.- Potential difference across the $ 2.00 \, \mu\text{F} $ capacitor: $\_\_\_\_\_$ \, V.Note: Fill in the blanks with the calculated values as you solve the problem.

Answered: For the system of capacitors shown in…

College Physics

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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**Capacitor System Analysis**

For the system of capacitors shown in the figure below, find the following. (Let $ C_1 = 9.00 \, \mu\text{F} $ and $ C_2 = 7.00 \, \mu\text{F} $.)

**Figure Explanation:**
- The diagram shows a circuit with three capacitors.
- $ C_1 = 9.00 \, \mu\text{F} $, $ C_2 = 7.00 \, \mu\text{F} $, and a third capacitor of $ 2.00 \, \mu\text{F} $.
- These capacitors are connected across a $ 90.0 \, \text{V} $ battery.

**Tasks:**

(a) **Find the equivalent capacitance of the system:**
- The equivalent capacitance is: $\_\_\_\_\_$ \, \mu\text{F}.

(b) **Determine the charge on each capacitor:**
- Charge on $ C_1 $: $\_\_\_\_\_$ \, \mu\text{C}.
- Charge on $ C_2 $: $\_\_\_\_\_$ \, \mu\text{C}.
- Charge on the $ 6.00 \, \mu\text{F} $ capacitor: $\_\_\_\_\_$ \, \mu\text{C}.
- Charge on the $ 2.00 \, \mu\text{F} $ capacitor: $\_\_\_\_\_$ \, \mu\text{C}.

(c) **Determine the potential difference across each capacitor:**
- Potential difference across $ C_1 $: $\_\_\_\_\_$ \, V.
- Potential difference across $ C_2 $: $\_\_\_\_\_$ \, V.
- Potential difference across the $ 6.00 \, \mu\text{F} $ capacitor: $\_\_\_\_\_$ \, V.
- Potential difference across the $ 2.00 \, \mu\text{F} $ capacitor: $\_\_\_\_\_$ \, V.

Note: Fill in the blanks with the calculated values as you solve the problem.

Expert Solution

Step 1

$G i v e n, C_{1} = 9 μ F C_{2} = 7 μ F L e t C_{3} = 6 μ F C_{4} = 2 μ F (a) T h e e q u i v a l e n t c a p a c i \tan c e o f t h e s y s t e m, F o r s e r i e s c o m b i n a t i o n, \frac{1}{C_{13}} = \frac{1}{9 μ F} + \frac{1}{6 μ F} C_{13} = 3.6 μ F L i k e w i s e, \frac{1}{C_{24}} = \frac{1}{2 μ F} + \frac{1}{7 μ F} C_{24} = 1.5555 μ F F o r p a r a l l e l c o m b i n a t i o n, C_{e q} = C_{24} + C_{13} C_{e q} = 1.5555 μ F + 3.6 μ F = 5.1555 μ F T h e e q u i v a l e n t c a p a c i t a n c e o f t h e s y s t e m = 5.1555 μ F$

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