No Problemmo #10
An electrical network of wires is formed by joining the grid points of two hexagons, as shown, where the resistance of each side and the connecting wires is An ideal battery of emf is joined at the bottom.
Considering that the wire connected with the cell is ideal, find the current passing through the battery.
Take and
For more exciting problems, try my set No Problemmo .
The answer is 3.
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Consider these currents on the loops
By kirchoff's voltage law (closed loops) we have that:
⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡ R − R 0 0 0 0 0 − R 4 ∗ R − R 0 0 0 − R 0 − R 4 ∗ R − R 0 0 0 0 0 − R 4 ∗ R − R 0 0 0 0 0 − R 4 ∗ R − R 0 0 0 0 0 − R 4 ∗ R − R 0 − R 0 0 0 − R 4 ∗ R ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤ ⋅ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡ I 1 I 2 I 3 I 4 I 5 I 6 I 7 ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤ = ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡ V 0 0 0 0 0 0 ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤ Solving this with your favorite method, mine is Cramer's rule, and we get that I 1 = 2 . 5 7 8 1 2 5 or I 1 ≈ 3 rounding to the nearest integer.