Problem 2

t=0

, an initially uncharged capacitor of capacitance

C

is connected in series with a resistor

R

and an ideal battery of emf

E

. Take current in the charging direction as positive and neglect internal resistance. Find the charge

q(t)

on the positive plate, current

i(t)

, and energy stored in the capacitor for

t\geq0

. Assume ideal components with constant values

R>0

C>0

, and

E>0

, a switch closed at

t=0

, and no initial capacitor charge. (a) Derive the differential equation from Kirchhoff’s loop rule. (b) Find

q(t)

and then the current, identifying the circuit time constant. (c) Find the capacitor energy and check the limits at

t=0

and as

t

becomes very large.

problems.proof.stepOf

\text{Check conservation, units, and limiting behavior}

problems.proof.analysis

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