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AP Physics 2
11.8 Resistor-Capacitor (RC) Circuits
AdvancedMCQGraphicalMathematicalProportional AnalysisConceptual25.1k
A quantitative line graph showing current \(I\) in amperes (A) on the vertical axis versus time \(t\) in milliseconds (ms) on the horizontal axis. The horizontal axis ranges from 0 to 15 ms with major ticks labeled every 1 ms (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15). The vertical axis ranges from 0 to 0.25 A with major ticks labeled every 0.05 A (0, 0.05, 0.10, 0.15, 0.20, 0.25). Grid lines are visible at every major tick mark. From \(t = 0\text{ ms}\) to \(t = 5\text{ ms}\), a smooth curve begins at (0, 0.20) and decays exponentially downward, reaching zero current at \(t = 5\text{ ms}\). At \(t = 5\text{ ms}\), a vertical dashed line extends from \(I = 0\) to \(I = 0.15\text{ A}\). From \(t = 5\text{ ms}\) to \(t = 15\text{ ms}\), a second curve begins at (5, 0.15) and decays exponentially downward toward zero current, reaching near zero around 15 ms. An annotation with a pointer arrow points to \(t = 5\text{ ms}\) with text reading 'Dielectric inserted'. No other labels, lines, text, or axes appear.
Current versus time for the RC circuit before and after dielectric insertion.
An uncharged parallel-plate capacitor is connected in series with a resistor of resistance \(R\) and an ideal DC voltage source of constant potential difference \(V_0\). At time \(t = 0\text{ ms}\), a switch is closed to begin charging the capacitor. At time \(t = 5\text{ ms}\), after the circuit has reached a steady state, a dielectric slab is rapidly inserted between the plates of the capacitor while it remains connected to the voltage source. The current \(I\) through the resistor as a function of time \(t\) is shown in the graph. Based on the graph, what is the dielectric constant \(\kappa\) of the inserted material?

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