A capacitor of capacitance

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Electricity, Magnetism & Electromagnetism · Electric current and circuits

Mathematical Methods for Physics, Ch First-order differential equations and physical modelling

Problem

A capacitor of capacitance C=220 μFC = 220\,\mu\mathrm{F}, initially uncharged, is charged through a resistor of resistance R=4.7 kΩR = 4.7\,\mathrm{k\Omega} from a constant 9.0 V9.0\,\mathrm{V} battery. Kirchhoff's loop rule gives q˙=(CV−q)/(RC)\dot{q} = (CV-q)/(RC), where q(t)q(t) is the charge on the capacitor. Solve the equation with q(0)=0q(0)=0 and find qq at t=2.0 st = 2.0\,\mathrm{s}.

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