Question

7 A circuit consists of a resistor of resistance R, and a capacitor of capacitance C, connected in series, and is described by the first order differential equation - + y = E where E is the constant e.m.f. and v is the voltage across the capacitor. Given that v(O) = 0, show by using the integrating factor method that v = E(1 - e-t/(RC))

Answer 1

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7 The given first ordon differential equation Re dv + v=E dr hc v = -6 This is a first ordu linear differential equatia in v Now, Integrating factor of = - e Shelt Re [R. Cane Constant Now, Now, multiplying both sides of by the Integrating facter e de vahel = (dame! ) - Vi e Re = & Re e Re + A Now, 86 = 0 Aiga Constant - 0 € RC. e +A = A=-E it it from ③ we have V. e Re = E. e Re - E [v = E(1- eRe ) Candy kitendesi [Proved 7 Re Dividing bothsides by Reit I rovee