A battery of emf ε, resistance R and capacitor C are connected in series; internal battery resistance is negligible. At t = 0, the capacitance is abruptly reduced by a factor η. If the subsequent current is [(η − x)ε/R] e⁻⁽ηᵗ⁄ᴿᶜ⁾, find x.
Physics · Mixed Chapter
JEE Mains

Question

A battery of emf ε, resistance R and capacitor C are connected in series; internal battery resistance is negligible. At t = 0, the capacitance is abruptly reduced by a factor η. If the subsequent current is [(η − x)ε/R] e⁻⁽ηᵗ⁄ᴿᶜ⁾, find x.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Explanation: Before the sudden change capacitor charge is Cε. Reducing capacitance by factor η raises its voltage instantaneously to ηε. The initial battery–capacitor voltage difference is (η−1)ε, giving current amplitude (η−1)ε/R. The new RC time constant is RC/η; comparing with the supplied expression gives x=1.