E - Handout #2
Bridge Circuit Matrix Analysis SOLUTION
ETME360 Spring 2014
R. Larson

 

Solve for eo using (a) Kirchoff’s Current Law (KCL) and (b) Kirchoff’s Voltage Law (KVL).  The KCL solution requires sketching in assumed currents through each resistor, then writing nodal equations.  The KVL solution uses assumed loop currents, and solves for the currents that are expressed as voltages and resistances:

You must use a  computer-based solver program (such as MATHCAD, MATLAB, EXCEL),  to create a computer generated printed matrix-format solution of the system of equations that you generate for this problem. (Hand-sketches of currents/voltage loops are OK, and manual equation development is expected.) You must include steps of equation development for full credit.

 SOLUTIONS:

Using Kirchoff"s Current Law:
Draw arbitrary current arrows, express in terms of voltage difference divided by resistance for each node:

...Find common denominator, move results to RH side and coefficients*unknowns to LH side.
In MATRIX form my equations look like this...

Using Kirchoff"s Voltage Law:
Draw arbitrary loop arrows, express in terms of currents times resistances in each loop:

Note that the sign convention on output voltages is somewhat arbitrary depending on setup: Magnitude of the solution is same either way.