Physics

Physics

Problem

A battery of emf EE is connected to resistor R1R_1 in series with a branch that contains resistor R2R_2 in parallel with an initially uncharged capacitor CC. The switch is closed at t=0t=0. Which statement correctly describes the current through R2R_2? a) It is non-zero at t=0t=0 but becomes zero after a long time. b) It is zero at all times because the capacitor completely bypasses R2R_2. c) It is zero at t=0t=0 but becomes non-zero after a long time. d) It is non-zero at all times, decreasing from an initial maximum to a smaller steady value.
Intuitive explanation

When the switch first closes, the uncharged capacitor acts like a short circuit—it greedily accepts charge and draws current away from R2R_2. Over time, as the capacitor charges up, it develops a voltage that opposes further charging, so current through R2R_2 increases. The key insight is that the capacitor and R2R_2 share the same voltage (they're in parallel), and you can use Kirchhoff's laws plus the capacitor equation Q=CVQ = CV to track how that shared voltage evolves from zero toward its steady-state value.

Intuitive explanation

When the switch first closes, the uncharged capacitor acts like a short circuit—it greedily accepts charge and draws current away from R2R_2. Over time, as the capacitor charges up, it develops a voltage that opposes further charging, so current through R2R_2 increases. The key insight is that the capacitor and R2R_2 share the same voltage (they're in parallel), and you can use Kirchhoff's laws plus the capacitor equation Q=CVQ = CV to track how that shared voltage evolves from zero toward its steady-state value.

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