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title: "An air-filled parallel-plate capacitor with plate area \\(A\\) and plate separation \\(d\\) has initial capacitance \\(C_0\\) and stores charge \\(Q_0\\) when connected to a battery of potential difference \\(V_0\\). While remaining connected to the battery, a slab of dielectric material with dielectric constant \\(\\kappa\\) and thickness \\(d\\) is inserted so that it fills half of the area between the plates, as shown in the figure. Which of the following correctly gives the new total capacitance \\(C’\\) of the capacitor and the new total stored charge \\(Q’\\) in terms of initial quantities and \\(\\kappa\\)?"
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url: "https://nerd-notes.com/ubq/117427/"
date_modified: "2026-08-04T06:52:06+00:00"
---

# An air-filled parallel-plate capacitor with plate area \(A\) and plate separation \(d\) has initial capacitance \(C_0\) and stores charge \(Q_0\) when connected to a battery of potential difference \(V_0\). While remaining connected to the battery, a slab of dielectric material with dielectric constant \(\kappa\) and thickness \(d\) is inserted so that it fills half of the area between the plates, as shown in the figure. Which of the following correctly gives the new total capacitance \(C’\) of the capacitor and the new total stored charge \(Q’\) in terms of initial quantities and \(\kappa\)?

An air-filled parallel-plate capacitor with plate area \(A\) and plate separation \(d\) has initial capacitance \(C_0\) and stores charge \(Q_0\) when connected to a battery of potential difference \(V_0\). While remaining connected to the battery, a slab of dielectric material with dielectric constant \(\kappa\) and thickness \(d\) is inserted so that it fills half of the area between the plates, as shown in the figure. Which of the following correctly gives the new total capacitance \(C'\) of the capacitor and the new total stored charge \(Q'\) in terms of initial quantities and \(\kappa\)?

![A schematic drawing showing a parallel-plate capacitor connected to an ideal battery of potential difference V_0. Two horizontal rectangular conducting plates of length L, width w, and vertical separation d are drawn parallel to each other. The top plate is connected by a wire to the positive terminal of a battery symbol labeled V_0, and the bottom plate is connected by a wire to the negative terminal. A solid shaded dielectric slab of dielectric constant \kappa, height d, length L/2, and width w is located inside the right half of the gap between the plates, completely filling the space from top to bottom plate on that side. The left half of the gap between the plates, of length L/2, is unshaded and empty. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785826326-UIFEPG.jpg)

- **A.** Capacitance: \(C' = \left(\dfrac{2\kappa}{\kappa + 1}\right) C_0\) | Stored charge: \(Q' = \left(\dfrac{2\kappa}{\kappa + 1}\right) Q_0\)
- **B.** Capacitance: \(C' = \kappa C_0\) | Stored charge: \(Q' = \kappa Q_0\)
- **C.** Capacitance: \(C' = \left(\dfrac{\kappa + 1}{2}\right) C_0\) | Stored charge: \(Q' = Q_0\)
- **D.** Capacitance: \(C' = \left(\dfrac{\kappa + 1}{2}\right) C_0\) | Stored charge: \(Q' = \left(\dfrac{\kappa + 1}{2}\right) Q_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117427/*