A method is presented for computing the equivalent resistance and the unknown components of simple series and parallel resistor networks. The approach consists in taking the product of a simple 2×2 matrix (N-1) times, where N is the total number of components in the network. The matrix approach originates from the study of continued fractions. Numerical computations only require an algorithm that handles matrix multiplication.
2. Mungan, C. E. and T. C. Lipscombe, "Babylonian resistor networks," Eur. J. Phys., 531-537, 2012.
3. Fry, T. C., "The use of continued fractions in the design of electrical networks," Elec. Net., 463-498, 1929.
4. Kagan, M., "On equivalent resistance of electrical circuits," Am. J. Phys., Vol. 83, 53-63, 2015.
5. Cserti, J., "Application of the lattice Greens function for calculating the resistance of an infinite network of resistors," Am. J. Phys., Vol. 68, 896-906, 2000.
6. De Carlo, R. and P.-M. Lin, Linear Circuit Analysis: Time Domain, Phasor, and Laplace Transform Approaches, Oxford University Press, USA, 2001.
7. Baak, D. A. V., "Variational alternatives to Kirchhov's loop theorem in dc circuits," Am. J. Phys., Vol. 67, 36-44, 1999.
8. Kreyszig , E., Advanced Engineering Mathematics, 5th Ed., Wiley & Sons, 1983.
9. Alexopoulos, A., "Binary circular inclusions in an effective medium approximation," Phys. Lett. A, 385-392, 2005.
10. Alexopoulos, A., "Quantum scattering via the discretisation of Schrodinger's equation," Phys. Lett. A, Vol. 363, 66-70, 2007.
11. Carmichael, R. D., The Theory of Numbers, and Diophantine Analysis, Dover, New York, 1959 .