A capacitor of capacitance charges through a resistor from a battery of e.m.f

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Mathematical Methods for Physics, Ch The derivative as a physical instrument

Problem

A capacitor of capacitance C=100 μFC = 100\,\mu\mathrm{F} charges through a resistor R=2.2 kΩR = 2.2\,\mathrm{k\Omega} from a battery of e.m.f. V0=9.0 VV_0 = 9.0\,\mathrm{V}. The voltage across the capacitor at time tt after the switch closes is V(t)=V0(1−e−t/RC).V(t) = V_0\left(1 - e^{-t/RC}\right). The charging current is I(t)=C dV/dtI(t) = C\,\mathrm{d}V/\mathrm{d}t. Find II at t=0.10 st = 0.10\,\mathrm{s}, treating RR and CC as ideal (no leakage, no lead resistance).

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