Q: Determine the Differential Equation for Response (vRtORiRt) in the circuit for t > 0.First thing you should do is LABELall the Voltages and Currentsin the circuit, use the following Notation:ResistorCapacitorInductorVoltagevRtvCtvLtCurrentiRtiCtiLtYou need to recognize Voltages and Currents that are EQUIVALENT in the circuit (Write them down):●Elements in Series → Same Currentflow through them●Elements in Parallel → Same Voltagedrop across themNow you can start writing your Differential Equation.STEP 1If the response you are looking for is a Voltage, the FIRST equation you write should be a KVL equation. To avoid any confusion, use the above Notation when writing the KVL equation.Likewise, if you are looking for a Current, the First equation should be a KCL equation.STEP 2Use Ohm's Law and Device Laws to Replace all other variables, LEAVE the Desired Response (vRt,iRt, etc.) and the Constants (Voltage and Current Sources) ALONE.
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Resistor, Electrical resistance, Electrical impedance