Are these Kirchhoff's junctions/nodes?
Determine the magnitude of the current "
" flowing across the bridge resistor (the one in the centre) and the equivalent resistance of the group of resistors "
". Enter your answer as the sum
.
(The numbers in purple near the resistors are the resistances in ohms.)
The answer is 1.95.
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1 solution
Call the voltages at the nodes to the left and right of the bridge V 1 and V 2 respectively. The currents out of these nodes must sum to zero, giving us two linear equations to solve for V 1 and V 2 :
1 V 1 − 1 0 + 6 V 1 − V 2 + 2 V 1 = 0 2 V 2 − 1 0 + 6 V 2 − V 1 + 3 V 2 = 0
After solving, it is simple to find the bridge current and total resistance, as shown below in the Mathcad capture. One cool thing to notice about the system matrix is that each diagonal term (corresponding to each node) is equal to the sum of the admittances connected to that node. And each off-diagonal term (corresponding to interactions between nodes) is equal to the negative of the admittance between the two nodes.