(R3+R10)/(R3*R10+R2*R10+R2*R3)*V+(R11+R)/(R11*R+R1*R11+R1*R)*V+((R2*R10*R11*R-R1*R3*R10*R-R1*R3*R10*R11+R2*R3*R11*R)*V)/(R1*R2*R3*R11+R2*R3*R11*R-R1*R3*R10*R-R1*R2*R10*R)*(1/R12+(R2+R3)/(R2*R3+R2*R10+R3*R10)+(R+R1)/(R*R1+R11*R+R*R11))=I;R1=10000;R2=10000;R3=100;R10=3900;R11=91000;R12=120

from sympy import symbols, Eq, solve

# Define the variables
R1, R2, R3, R10, R11, R12, R, V, I = symbols('R1 R2 R3 R10 R11 R12 R V I')

# Define the equation based on the user's input
equation = Eq(
    (R3 + R10) / (R3 * R10 + R2 * R10 + R2 * R3) * V +
    (R11 + R) / (R11 * R + R1 * R11 + R1 * R) * V +
    ((R2 * R10 * R11 * R - R1 * R3 * R10 * R - R1 * R3 * R10 * R11 + R2 * R3 * R11 * R) * V) /
    (R1 * R2 * R3 * R11 + R2 * R3 * R11 * R - R1 * R3 * R10 * R - R1 * R2 * R10 * R) *
    (1 / R12 + (R2 + R3) / (R2 * R3 + R2 * R10 + R3 * R10) + (R + R1) / (R * R1 + R11 * R + R * R11))
    , I
)

# Substitute given values into the equation
substitutions = {R1: 10000, R2: 10000, R3: 100, R10: 3900, R11: 91000, R12: 120}

# Solve the equation for I
I_solution = solve(equation.subs(substitutions), I)
I_solutionThe solution for \( I \) in terms of \( V \) and \( R \) after substituting the given resistor values is:

\[
I = \frac{V \cdot (-1879543413319 \cdot R^3 - 16753421952589000 \cdot R^2 + 1454623018940000000 \cdot R + 10034087700000000000)}{775488000 \cdot R \cdot (23533 \cdot R^2 + 141330000 \cdot R - 637000000000)}
\]

This expression relates the current \( I \) to the voltage \( V \) and the resistance \( R \).

If you have specific values for \( V \) and \( R \), I can calculate the numerical value of \( I \).

Would you like to proceed with that? 

---

Here are five follow-up questions that might be useful:
1. Would you like to solve for \( R \) if you have a specific value for \( I \) and \( V \)?
2. Should we explore a range of values for \( R \) to see how it affects \( I \)?
3. Do you need a simplified expression for \( I \) by considering some limits or assumptions for \( R \)?
4. Would you like to visualize the relationship between \( I \), \( V \), and \( R \)?
5. Do you need further clarification on how the resistances were substituted and their impact?

**Tip**: Solving circuit equations symbolically can help identify key relationships between parameters before plugging in numerical values.

Explore the solution for a complex electrical equation involving resistances (R1 = 10,000Ω, R2 = 10,000Ω, R3 = 100Ω, R10 = 3,900Ω, R11 = 91,000Ω, R12 = 120Ω), voltage (V), and current (I). Understand the relationship between voltage, current, and resistances using symbolic algebraic methods.

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