A DC bridge circuit is shown below. Suppose we are interested in solving for the

Question

A DC bridge circuit is shown below. Suppose we are interested in solving for the voltages at the nodes labeled 1 through 3. The node labeled 0 is the ground or reference node and all voltages are expressed with respect to this node. Once the node voltages are known the current, I, through any resistor can be computed using Ohm's law, I = V/R where V denotes the voltage drop across the resistor, R. Let v_k denote the voltage at node k for 1 lessthanorequalto k lessthanorequalto 3. The relationships between the node voltages are obtained by applying Kirchhoff's current law, which says that the sum of the currents leaving each node must be zero. This yields a system of three equations in three unknowns. Assume R_s = 10 ohm, the load resistance is R_L = 1000 ohm, the bridge resistances are R_1 = 220 ohm, R_2 = 330 ohm, R_3 = 470 ohm, and R_4 = 560 ohm. The applied voltage is E = 12 V. Find the voltages at the three internal nodes using Gauss-Seidel iteration with epsilon lessthanorequalto 0.0001.

Explanation / Answer

Apply nodal analysis at node V1.

{(V1-12)/10}+{(v1-v2)/220}+{(v1-v3)/330}=0

V1{(1/10)+(1/220)+(1/330)}+v2{-1/220}+v3{-1÷330}=12/10

Apply nodal analysis at node v2.

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