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title: "A circuit consists of an ideal battery of potential difference \\(\\varepsilon\\), an open switch, a resistor of resistance \\(R\\), and an uncharged parallel-plate air capacitor of capacitance \\(C_0\\) connected in a single loop. The switch is closed at time \\(t = 0\\), and at a later time \\(t_1\\) while the capacitor is still charging, a slab of dielectric constant \\(\\kappa > 1\\) is rapidly slid between the plates to completely fill the space in a negligible time interval. An ammeter in series with the resistor records an abrupt, finite increase in current at \\(t_1\\). Which of the following provides the correct physical explanation for this sudden jump in current?"
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url: "https://nerd-notes.com/ubq/124779/"
date_modified: "2026-09-28T14:11:14+00:00"
---

# A circuit consists of an ideal battery of potential difference \(\varepsilon\), an open switch, a resistor of resistance \(R\), and an uncharged parallel-plate air capacitor of capacitance \(C_0\) connected in a single loop. The switch is closed at time \(t = 0\), and at a later time \(t_1\) while the capacitor is still charging, a slab of dielectric constant \(\kappa > 1\) is rapidly slid between the plates to completely fill the space in a negligible time interval. An ammeter in series with the resistor records an abrupt, finite increase in current at \(t_1\). Which of the following provides the correct physical explanation for this sudden jump in current?

A circuit consists of an ideal battery of potential difference \(\varepsilon\), an open switch, a resistor of resistance \(R\), and an uncharged parallel-plate air capacitor of capacitance \(C_0\) connected in a single loop. The switch is closed at time \(t = 0\), and at a later time \(t_1\) while the capacitor is still charging, a slab of dielectric constant \(\kappa > 1\) is rapidly slid between the plates to completely fill the space in a negligible time interval. An ammeter in series with the resistor records an abrupt, finite increase in current at \(t_1\). Which of the following provides the correct physical explanation for this sudden jump in current?

![A rectangular schematic of a single-loop circuit drawn in black wire lines. The left vertical branch contains an ideal DC source labeled \(\varepsilon\) with a longer top horizontal bar and a shorter bottom bar. The top horizontal branch contains an open knife switch followed by a zigzag resistor labeled \(R\). The right vertical branch contains a parallel-plate capacitor with two horizontal parallel plates labeled \(C_0\). A shaded gray rectangular slab labeled \(\kappa\) is positioned to the right of the capacitor plates, with a horizontal arrow pointing leftward into the gap between the plates. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604674-DpZKav.jpg)

- **A.** The dielectric's bound polarization charge immediately draws a burst of extra free charge through the circuit to maintain electric field continuity across the gap, thereby creating a transient surge in current through the resistor.
- **B.** The potential difference across the capacitor remains continuous during the rapid insertion, forcing the rate of charge delivery to scale in proportion to the new capacitance according to \(I = \kappa C_0 (dV_C/dt)\), which causes the current to step upward.
- **C.** The insertion increases the circuit time constant to \(\kappa R C_0\), which slows the rate of charge accumulation and resets the circuit to a state equivalent to an earlier moment in the charging cycle, raising the current to its previous level.
- **D.** The free charge on the plates remains continuous because finite resistance prevents instantaneous charge transfer, so the increased capacitance abruptly reduces the capacitor's potential difference, which increases the voltage drop across the resistor and raises the current.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124779/*