To understand the behavior of the current and voltage in a simple R-C circuit A capacitor with capacitance C is initially charged with charge q0. At time t=0 a resistor with resistance R is connected across the capacitor

PART A

Use the Kirchhoff loop rule and Ohm's law to express the voltage across the capacitor V(t) in terms of the current I(t) flowing through the circuit

PART B

We would like to use the relation V(t) = I(t)R to find the voltage and current in the circuit as functions of time. To do so, we use the fact that current can be expressed in terms of the voltage. This will produce a differential equation relating the voltage V(t) to its derivative. Rewrite the right-hand side of this relation, replacing I(t) with an expression involving the time derivative of the voltage.