Resistance network calculator
- Introduction
Calculate the resistance of any resistor network.
- The network is stated with a string.
- The resistors are separated by a vertical dash.
- Each resistor has
- a starting node
- an ending node
- a resistance
- Background
- Regular 3x3 mesh, using twelve one ohm resistors
0 - 1 - 2 | | | 3 - 4 - 5 | | | 6 - 7 - 8
Battery connection nodes: 0 and 8
assert 3/2 == network(9,0,8,"0 1 1|1 2 1|3 4 1|4 5 1|6 7 1|7 8 1|0 3 1|3 6 1|1 4 1|4 7 1|2 5 1|5 8 1")
- Regular 4x4 mesh, using 24 one ohm resistors
0 - 1 - 2 - 3 | | | | 4 - 5 - 6 - 7 | | | | 8 - 9 -10 -11 | | | | 12 -13 -14 -15
Battery connection nodes: 0 and 15
assert 13/7 == network(16,0,15,"0 1 1|1 2 1|2 3 1|4 5 1|5 6 1|6 7 1|8 9 1|9 10 1|10 11 1|12 13 1|13 14 1|14 15 1|0 4 1|4 8 1|8 12 1|1 5 1|5 9 1|9 13 1|2 6 1|6 10 1|10 14 1|3 7 1|7 11 1|11 15 1")
- Ten resistor network
Battery connection nodes: 0 and 1
assert 10 == network(7,0,1,"0 2 6|2 3 4|3 4 10|4 5 2|5 6 8|6 1 4|3 5 6|3 6 6|3 1 8|2 1 8")
- Wheatstone network
This network is not possible to solve using the previous Resistance Calculator as there is no natural starting point.
assert 180 == network(4,0,3,"0 1 150|0 2 50|1 3 300|2 3 250")
Go
<lang go>package main
import (
"fmt" "math/big" "strconv" "strings"
)
func gauss(a [][]*big.Rat, b []*big.Rat) []*big.Rat {
n := len(a) t := new(big.Rat) u := new(big.Rat) for i := 0; i < n; i++ { t.Abs(a[i][i]) k := i for j := i + 1; j < n; j++ { if u.Abs(a[j][i]).Cmp(t) == 1 { t.Abs(a[j][i]) k = j } } if k != i { for j := i; j < n; j++ { u.Set(a[i][j]) a[i][j].Set(a[k][j]) a[k][j].Set(u) } u.Set(b[i]) b[i].Set(b[k]) b[k].Set(u) } t.Set(u.Inv(a[i][i])) for j := i + 1; j < n; j++ { a[i][j].Mul(a[i][j], t) } b[i].Mul(b[i], t) for j := i + 1; j < n; j++ { t.Set(a[j][i]) for k := i + 1; k < n; k++ { u.Mul(t, a[i][k]) a[j][k].Sub(a[j][k], u) } u.Mul(t, b[i]) b[j].Sub(b[j], u) } } for i := n - 1; i >= 0; i-- { for j := 0; j < i; j++ { u.Mul(a[j][i], b[i]) b[j].Sub(b[j], u) } } return b
}
func network(n, k0, k1 int, s string) *big.Rat {
a := make([][]*big.Rat, n) for i := 0; i < n; i++ { a[i] = make([]*big.Rat, n) for j := 0; j < n; j++ { a[i][j] = new(big.Rat) } } arr := strings.Split(s, "|") for _, resistor := range arr { rarr := strings.Fields(resistor) n1, _ := strconv.Atoi(rarr[0]) n2, _ := strconv.Atoi(rarr[1]) ri, _ := strconv.Atoi(rarr[2]) r := new(big.Rat).SetFrac64(1, int64(ri)) a[n1][n1].Add(a[n1][n1], r) a[n2][n2].Add(a[n2][n2], r) if n1 > 0 { a[n1][n2].Sub(a[n1][n2], r) } if n2 > 0 { a[n2][n1].Sub(a[n2][n1], r) } } a[k0][k0].SetInt64(1) b := make([]*big.Rat, n) for i := 0; i < n; i++ { b[i] = new(big.Rat) } b[k1].SetInt64(1) return gauss(a, b)[k1]
}
func main() {
var ra [4]*big.Rat ra[0] = network(7, 0, 1, "0 2 6|2 3 4|3 4 10|4 5 2|5 6 8|6 1 4|3 5 6|3 6 6|3 1 8|2 1 8") ra[1] = network(9, 0, 8, "0 1 1|1 2 1|3 4 1|4 5 1|6 7 1|7 8 1|0 3 1|3 6 1|1 4 1|4 7 1|2 5 1|5 8 1") ra[2] = network(16, 0, 15, "0 1 1|1 2 1|2 3 1|4 5 1|5 6 1|6 7 1|8 9 1|9 10 1|10 11 1|12 13 1|13 14 1|14 15 1|0 4 1|4 8 1|8 12 1|1 5 1|5 9 1|9 13 1|2 6 1|6 10 1|10 14 1|3 7 1|7 11 1|11 15 1") ra[3] = network(4, 0, 3, "0 1 150|0 2 50|1 3 300|2 3 250") for _, r := range ra { s := r.String() if strings.HasSuffix(s, "/1") { fmt.Println(s[0 : len(s)-2]) } else { fmt.Println(s) } }
}</lang>
- Output:
10 3/2 13/7 180
Python
<lang python>from fractions import Fraction
def argmax(m,i): col = [abs(row[i]) for row in m] return col.index(max(col))
def gauss(m): n, p = len(m), len(m[0]) for i in range(n): k = i + argmax(m[i:n],i) if k != i: m[i], m[k] = m[k], m[i] t = 1 / m[i][i] for j in range(i + 1, p): m[i][j] *= t for j in range(i + 1, n): t = m[j][i] for k in range(i + 1, p): m[j][k] -= t * m[i][k] for i in range(n - 1, -1, -1): for j in range(i): m[j][-1] -= m[j][i] * m[i][-1] return [row[-1] for row in m]
def network(n,k0,k1,s): I = Fraction(1, 1) m = [[0] * (n+1) for i in range(n)] resistors = s.split('|') for resistor in resistors: a,b,r = resistor.split(' ') a,b,r = int(a), int(b), Fraction(1,int(r)) m[a][a] += r m[b][b] += r if a > 0: m[a][b] -= r if b > 0: m[b][a] -= r m[k0][k0] = I m[k1][-1] = I return gauss(m)[k1]
assert 10 == network(7,0,1,"0 2 6|2 3 4|3 4 10|4 5 2|5 6 8|6 1 4|3 5 6|3 6 6|3 1 8|2 1 8") assert 3/2 == network(3*3,0,3*3-1,"0 1 1|1 2 1|3 4 1|4 5 1|6 7 1|7 8 1|0 3 1|3 6 1|1 4 1|4 7 1|2 5 1|5 8 1") assert Fraction(13,7) == network(4*4,0,4*4-1,"0 1 1|1 2 1|2 3 1|4 5 1|5 6 1|6 7 1|8 9 1|9 10 1|10 11 1|12 13 1|13 14 1|14 15 1|0 4 1|4 8 1|8 12 1|1 5 1|5 9 1|9 13 1|2 6 1|6 10 1|10 14 1|3 7 1|7 11 1|11 15 1") assert 180 == network(4,0,3,"0 1 150|0 2 50|1 3 300|2 3 250")</lang>