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A circuit consisting of a resistor, capacitor and power supply is called an RC circuit. Physics...

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Advance Math

A circuit consisting of a resistor, capacitor and power supplyis called an RC circuit. Physics and Kirchoff’s laws imply that ifQ is the charge on the capacitor, R is the resistance and E is thepower supply, then R(dQ/dt) + (1/C)Q = E. Let R = 20, C = .1 and E= 100e ?.1t. If there is no charge on the capacitor at time t=0,find the charge Q at any time after that.

In an RL circuit, as described in class, R = .1, L = 1 and E =10(1 ? e ?.05t ). If there is no current in the circuit at time t =0, find the current at any time after that.

Solve the initial value problem dy/dt = 1 ? 5y/(150 ? 2t) , y(0)= 5. NOTE: Since we only care about what is going on up to when thetank is empty (i.e., t < 75 minutes), you can assume 150 ? 2t> 0.

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