### Parallel-Plate Capacitor AnalysisA 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 DescriptionThe 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:** \[ \boxed{\text{J}} \]

a. Write the expression for capacitance of the parallel plate capacitor with dielectric.

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?

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?

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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:**
\[
\boxed{\text{J}}
\]

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