Question

An isolated capacitor of unknown capacitance has been charged to a potential difference of 100 $\mathrm{V}$ . When the charged capacitor is then connected in parallel to an uncharged $10.0-\mu \mathrm{F}$ capacitor, the potential difference across the combination is 30.0 $\mathrm{V}$ . Calculate the unknown capacitance.

Name: Problem 67, Chapter 26: Physics for Scientists and Engineers with Modern Physics
Uploaded: 2020-08-01T20:41:53-08:00
Duration: 50 s
Channel: Mayukh Banik
Description: An isolated capacitor of unknown capacitance has been charged to a potential difference of 100 V . When the charged capacitor is then connected in parallel to an uncharged 10.0-μF capacitor, the potential difference across the combination is 30.0 V . Calculate the unknown capacitance.

   An isolated capacitor of unknown capacitance has been charged to a potential difference of 100 $\mathrm{V}$ . When the charged capacitor is then connected in parallel to an uncharged $10.0-\mu \mathrm{F}$ capacitor, the potential difference across the combination is 30.0 $\mathrm{V}$ . Calculate the unknown capacitance.

Physics for Scientists and Engineers with Modern Physics

Paul Tipler, Gene… 6th Edition

Chapter 26, Problem 67

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Solved by Expert Mayukh Banik

08/01/2020

Step 1

We have an isolated capacitor with an unknown capacitance $ C_x $ charged to a potential difference of 100 V. The charge on this capacitor can be expressed as $ Q_x = C_x \times 100 $. Show more…

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An isolated capacitor of unknown capacitance has been charged to a potential difference of 100 $\mathrm{V}$ . When the charged capacitor is then connected in parallel to an uncharged $10.0-\mu \mathrm{F}$ capacitor, the potential difference across the combination is 30.0 $\mathrm{V}$ . Calculate the unknown capacitance.

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Key Concepts

Parallel Capacitor Configuration

When capacitors are connected in parallel, they all experience the same voltage across their terminals. The total capacitance of the system is the sum of the individual capacitances, which affects how charges redistribute when connected to each other.

Conservation of Charge

The conservation of charge principle states that in an isolated system, the total electric charge remains constant. When a charged capacitor is connected to an uncharged capacitor, the charge redistributes between them without any loss, allowing calculations based on the initial and final voltage conditions.

Capacitance

Capacitance is a measure of a capacitor's ability to store electrical charge per unit voltage. It defines the relationship between the charge stored on the capacitor and the voltage across it, typically expressed in Farads.

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