- #1

terence cheng

- 3

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**Hi I got stuck at the following circuit problem which involves linear algebra, since I am not a physics major, I don't even have the basics to get started. Please shed some light, really appreciate it! Thanks a lot.**

1. Homework Statement

1. Homework Statement

Consider a long chain of resistors wired up like this

All the resistors have the same resistance R. The power rail at the top is at voltage V+ = 5V. The problem is to find the voltages V1 . . . VN at the internal points in the circuit.

Using Ohm’s law and the Kirchhoff current law, which says that the total net current flow out of (or into) any junction in a circuit must be zero, show that the voltages V1 . . . VN satisfy the equations

3V1 − V2 − V3 = V+,

−V1 + 4V2 − V3 − V4 = V+,

... −Vi−2 − Vi−1 + 4Vi − Vi+1 − Vi+2 = 0, ...

−VN−3 − VN−2 + 4VN−1 − VN = 0,

−VN−2 − VN−1 + 3VN = 0.

Express these equations in vector form

**and find the values of the matrix**

*Av = w***and the vector**

*A***.**

*w*## Homework Equations

## The Attempt at a Solution

I considered when N = 2, it gives me a "Wheatstone bridge" with V1 = V2 = V/2

but then how should i continue? thanks a lot![/B]