A parallel-plate capacitor has square plates of side s = 2.30 cm and plate separation d = 3.00 mm. The capacitor is charged by a battery to a charge Q = 4.50 µc, after which the battery is disconnected. A porcelain dielectric (x = 6.5) is then inserted a distance y = 1.00 cm into the capacitor (see figure below). Hint: Consider the system as two capacitors connected in parallel. Dielectric K (a) What is the effective capacitance of this capacitor? pF (b) How much energy is stored in the capacitor?

Physics for Scientists and Engineers with Modern Physics
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Chapter26: Current And Resistance
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Problem 45AP: Review. A parallel-plate capacitor consists of square plates of edge length that are separated by a...
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### Parallel-Plate Capacitor Analysis

A parallel-plate capacitor consists of two square plates with a side length of \(s = 2.30 \, \text{cm}\) and a plate separation of \(d = 3.00 \, \text{mm}\). The capacitor is initially charged by a battery to a charge \(Q = 4.50 \, \mu\text{C}\), after which the battery is disconnected. Subsequently, a porcelain dielectric \((\kappa = 6.5)\) is inserted into the capacitor to a distance \(y = 1.00 \, \text{cm}\) as illustrated in the figure below.

#### Diagram Description

The provided figure presents a parallel-plate capacitor:

- The left plate is positively charged with \(+Q\) and the right plate is negatively charged with \(-Q\).
- A dielectric material partially fills the space between the plates, occupying a distance \(y\) from the bottom.
- The dimensions and positions are clearly marked:
  - \(s\) represents the side of the square plates.
  - \(d\) represents the separation distance between the plates.
  - \(y\) signifies the portion of the plate separation filled by the dielectric.

#### Questions

(a) **Determine the effective capacitance of this capacitor:**
   \[
   \boxed{\text{pF}}
   \]

(b) **Calculate the energy stored in the capacitor:**
   \[
   \boxed{\text{J}}
   \]
Transcribed Image Text:### Parallel-Plate Capacitor Analysis A parallel-plate capacitor consists of two square plates with a side length of \(s = 2.30 \, \text{cm}\) and a plate separation of \(d = 3.00 \, \text{mm}\). The capacitor is initially charged by a battery to a charge \(Q = 4.50 \, \mu\text{C}\), after which the battery is disconnected. Subsequently, a porcelain dielectric \((\kappa = 6.5)\) is inserted into the capacitor to a distance \(y = 1.00 \, \text{cm}\) as illustrated in the figure below. #### Diagram Description The provided figure presents a parallel-plate capacitor: - The left plate is positively charged with \(+Q\) and the right plate is negatively charged with \(-Q\). - A dielectric material partially fills the space between the plates, occupying a distance \(y\) from the bottom. - The dimensions and positions are clearly marked: - \(s\) represents the side of the square plates. - \(d\) represents the separation distance between the plates. - \(y\) signifies the portion of the plate separation filled by the dielectric. #### Questions (a) **Determine the effective capacitance of this capacitor:** \[ \boxed{\text{pF}} \] (b) **Calculate the energy stored in the capacitor:** \[ \boxed{\text{J}} \]
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