A three-branch circuit has branch currents ,

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Electricity, Magnetism & Electromagnetism · Linear algebra and vector spaces

Mathematical Methods for Physics, Ch Matrices, determinants and systems of linear equations

Problem

A three-branch circuit has branch currents I1I_1, I2I_2, I3I_3 obeying the junction rule I1=I2+I3I_1 = I_2 + I_3 and the two mesh equations 6I1+5I2=86I_1 + 5I_2 = 8 and −5I2+5I3=1-5I_2 + 5I_3 = 1 (currents in amperes, the numbers on the right in volts, the coefficients in ohms). (a) Write the three equations as AI=b\mathsf{A}\mathbf{I} = \mathbf{b}. (b) Solve for I1I_1, I2I_2, I3I_3 by Gaussian elimination. (c) Check the result by substituting back into all three original equations.

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