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Step Response of First Order RC and RL Circuits 

Section 1 Section 2 Section 3 Section 4 Section 5 Section 6
Section 7 Section 8 Questionnaire Results page 
Step response of an RL CircuitIn calculating the step response of an RL circuit we consider the following circuit: After the above switch is closed Kirchoffs' voltage law can be applied which gives: Then rearranging the above we obtain the following equation: We now integrate each side and using x and y as variables for the integration we get: thus integrating this gives: where I_{0 }is the current at time t=0 and i(t) is the current at any time after 0. Taking inverse logs and rearranging gives us the following equation: When the initial energy in the inductor is 0, I_{0} is zero hence the above becomes: Step Response of a RC circuitIf we consider the following circuit: we can use a method similar to that of above to arrive at the expression for the voltage, which is: 

© Mark Whiteley 2002 