# math 307 and about the differential equation

10.+ -/2 pointsMy NotesR<v (t)Kirkhoff’s law states that the sum of the voltage drops around a closed loop is zero. If you start at the top of the Voltage source V(t) and follow the arrows around the loop, you pass through the resistor R, the capacitor C, and finally through the voltageCsource V(t) .The voltage drop across the resistor is the product of the (constant) resistance R of the resistor, and the current I(t) passing through the resistor.The voltage drop across a capacitor is equal to , where q(t) is the charge on the capacitor, and the constant C is the capacitance of the capacitor.Across a voltage source (typically a battery or a power supply), the voltage increases by V(t) , so the voltage drop is is -V(t) .The current passing through the resistor and the charge on the capacitor are related by the equation I = da/dt .Write a differential equation for the charge q(t) on the capacitor as a function of time. Your answer should depend on q, V , and the constants R and C, but not on I . In your answer, write just q and V for the functions q(t) and V(t) . Remember to insert a space or explicitly type”*” between two letters to indicate multiplication.dadtWrite a differential equation for the voltage drop Vc(t) across the capacitor as a function of time t . In your answer, write just Vc and V for the functions Vo(t) and V(t) .dVC =at