# Nodal analysis help

## Homework Statement

Using nodal analisis we need obtain the differential equation

2. The attempt at a solution

For I1 and take the point under C as reference, but i am stuck on it

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NascentOxygen
Staff Emeritus
Hi Jair Gutierrez.

The next step here is to add those 3 currents, and equate the result to 0; this gives you your second order DE.

You don't have the right expression for I1, the current in an inductor.

gneill
Mentor
Is Va entirely arbitrary or does it have some particular form? I'm assuming it's a source rather than the desired output from some initial value conditions of the circuit... the problem statement is rather vague.

Hi thanks for your anwers, yes I1 is an inductor,
I1=integral of (Va-V1)/L, but in all this equations where i use the resistor R, i think R is part of I1, but i dont know how write the equation in this case.

Here is the original exercise, 5.15

In my node i have 3 currents, I1, I2, I3, i think R is part of I1, but how I involve R1 to form part of the equation for I1

gneill
Mentor
The potential at the left side of L1 is not Va since, as you say the resistor R is between it and the reference node. There will be a potential drop across R due to $I_1$. So the potential across L1 is going to be something like: $(-I_1 R + V_a - V_1)$.