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Determine Differential Equation

# Determine Differential Equation - Q Determine the...

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Q: Determine the Differential Equation for Response ( v R t OR i R t ) in the circuit for t > 0. First thing you should do is LABEL all the Voltages and Currents in the circuit, use the following Notation: Resistor Capacitor Inductor Voltage v R t v C t v L t Current i R t i C t i L t You need to recognize Voltages and Currents that are EQUIVALENT in the circuit (Write them down): Elements in Series → Same Current flow through them Elements in Parallel → Same Voltage drop across them Now you can start writing your Differential Equation. STEP 1 If 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 2 Use Ohm's Law and Device Laws to Replace all other variables, LEAVE the Desired Response ( v R t , i R t , etc.) and the Constants (Voltage and Current Sources) ALONE.
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