Question 2 An electric circuit consists of a battery (voltage source) connected to a resistor and capacitor in series. The resulting ordinary differential equation for the voltage on the capacitor Ve(t) is as follows: dVo_ Vin at RO Ro c(t). R VR Vin We will use the values 1 C - 0.001 - 1000 Vin = 9 Here resistance R is in Ohms, time t is in seconds, capacitance C is in Farads, and voltage Vin is in Volts. Initially, the voltage on the capacitor is zero: Va (0) = 0. (a) (2 marks) Assume the resistance is constant: R = 100. Check by direct substitution that the function Vo(t) = 9(1 - e-10t) satisfies the ODE and the initial condition. (b) (4 marks) Now assume that the resistor slowly degrades, so that its resistance increases with time: R = R(t) = 100 + 2t. Solve the ordinary differential equation for Vo(t) with this resistance, using either separation of variables, or the integrating factor method. Make sure to also include the initial condition