Hello everyone,
I am trying to figure out the equivalent resistance of a honeycomb circuit of resistors (cf image attached, where each resistor has the same value).
In the example on the image, there are 3 nodes on the horizontal axis (Nx=3), and 14 nodes on the vertical axis (Ny=14), but I would like to know if there is an analytical solution for any numbers of nodes along both axes (for any Nx and Ny).
The solution for Nx=1 is quite trivial, it is simply: Req=Ny*R.
But do you think it is possible to find an analytical solution for Req as a function of Nx, Ny and R?
If yes, how would you proceed?
If no, what methods do you suggest for computing this?
I was thinking using a program, in which you input one equation for each node and each loop (Kirchoff's laws) and having a variable for each current in each resistor. And then having a program that could analytically solve the system of equation (using matrices for examples). Can you think of something better/faster/easier?
Thank you in advance for your help and time!
Best,
Julia
I am trying to figure out the equivalent resistance of a honeycomb circuit of resistors (cf image attached, where each resistor has the same value).
In the example on the image, there are 3 nodes on the horizontal axis (Nx=3), and 14 nodes on the vertical axis (Ny=14), but I would like to know if there is an analytical solution for any numbers of nodes along both axes (for any Nx and Ny).
The solution for Nx=1 is quite trivial, it is simply: Req=Ny*R.
But do you think it is possible to find an analytical solution for Req as a function of Nx, Ny and R?
If yes, how would you proceed?
If no, what methods do you suggest for computing this?
I was thinking using a program, in which you input one equation for each node and each loop (Kirchoff's laws) and having a variable for each current in each resistor. And then having a program that could analytically solve the system of equation (using matrices for examples). Can you think of something better/faster/easier?
Thank you in advance for your help and time!
Best,
Julia