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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 Spring '08
 FOWLER
 Volt, Resistor, Electrical resistance, Electrical impedance

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