Answered: Vin dt RC dVc 1 RC Vc(t).

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Vin dt RC dVc 1 RC Vc(t).

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Question

we have a voltage source (battery) connected to a resistor and capacitor in series. Differential equation for voltage of capacitor Vc(t) is attached.

C = 0.001, Vin = 9

a) Assume R = 100 ohms, check with direct substitution that Vc(t) = 9*(1 - e^(-10t)), satisfies the ode and initial condition.

b) Assuming resistance increases with time; R = R(t) = 100+2t, solve ordinary differential equation for Vc(t), using one of two methods: seperation of variables, or integrating factor method.

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Step 1: Given the voltage sources connected to resistor and capacitor in series

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Step 2: R = R(t) = 100+2t, solve ordinary differential equation for Vc(t),

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Follow-up Questions

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Follow-up Question

in part a, what does the I.F equal before e^10t? having trouble reading it

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