Chapter 9.5, Problem 37E

RC circuit equation Suppose a battery with voltage V is connected in series to a capacitor (a charge storage device) with capacitance C and a resistor with resistance R. As the charge Q in the capacitor increases, the current I across the capacitor decreases according to the following initial value problems. Solve each initial value problem and interpret the solution.

 a.     $I^{\prime }(t)+\frac{1}{RC}I(t)=0,I(0)=\frac{V}{R}$

 b.     $Q^{\prime }(t)+\frac{1}{RC}Q(t)=\frac{V}{R},Q(0)=0$