Setup an Electrical Circuit - Guidance Needed

[Dustinsfl]

I haven't set up a DE for an electrical system since 2008 so I need some guidance until I get the hang of it again.

The circuit in question is:

http://imagizer.imageshack.us/v2/800x600q90/594/0sze.png

 

[gtoguy97]

There are a few steps to setting up a differential equation from an electrical system:1. Identify the circuit's components and label them accordingly.2. Formulate the KVL (Kirchhoff's Voltage Law) equation for the circuit. This equation is the sum of the voltage drops around the loop, which must be zero.3. Use Ohm’s law (V=IR) to express the current in each branch in terms of the voltages and resistances.4. Rearrange the equations to solve for the unknown currents.5. Substitute the currents back into the KVL equation to obtain the differential equation.For this particular circuit, the KVL equation can be written as V1 - V2 - IR1 - IR2 = 0. Using Ohm's law, we can express the currents in terms of the voltages and resistances:I1 = (V1 - V2)/R1I2 = V2/R2Substituting these back into the KVL equation, we get: V1 - V2 - (V1 - V2)R1/R1 - V2R2/R2 = 0Which simplifies to:V1 - V2(1 + R2/R1) = 0Therefore, the differential equation for this circuit is:dV1/dt - dV2/dt(1 + R2/R1) = 0