Math and Arithmetic
Electronics Engineering
Electrical Engineering

Use second order differential equation to solve RCL series circuit?


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we use charge stored in the capacitor as our variable (remember it one of the three variable). so the potential difference across the capacitor is --charge stored in the capacitor at that instance/capacitance of the capacitor. potential difference across resistor is --resistance* differential of charge with respect to time. potential difference across inductor is -- inductance*double difference of charge with respect to the time. If there is no voltage source attached with the network then sum of the total potential difference is equal to zero hence your solution.........L*d^2(q)/dt^2 + R*d(q)/dt + q/c =0