Node Method Problem: Identifying Errors

LongApple · Jan 19, 2015

Homework Statement

Circuit schematic of a network with two voltage sources V1 and V2 and three resistors R1, R2 and R3, with loop currents i1 and i2 and the voltage v3 across R3 marked.

Form with six input fields for coefficients a1, a2, b1, b2, c1 and c2, each marked with a red X and showing an incorrect expression beside it, such as R2*R3/(R1*R2+R1*R3+R2*R3) for a1.

Homework Equations

V=IR

The Attempt at a Solution

Handwritten node-voltage derivation for a circuit with resistors R1, R2 and R3 and voltage sources V1 and V2, ending with the expression for V3 as a ratio of sums of resistor products.

$Handwritten red-ink derivation of nodal analysis: (v3 - v1)/R1 = i1, then i1 expressed as a fraction in V1 and V2 with R1, R2, R3 terms, split into coefficient brackets for V1 and V2.$

I believe my a1 and a2 are correct.

But my b1 is definitely wrong. Even if I carry out the above subtraction for the v1 part (which gives you b1) I will not have somethign as simple as R2 + R3 on the numerator

Web form showing the label b1 = followed by an empty answer box and the entered expression -(R2+R3)/(R1*R2+R1*R3+R2*R3), marked with a red X for incorrect.

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Where would be some starting places to pinpoint the error?

LongApple · Jan 19, 2015

I'll try putting in dark blue.

Is this any easier to read?

I cannot change some of the below because some of it is pasted images

Handwritten circuit analysis with a red-marked schematic of three resistors R1, R2, R3 with voltage sources V1 and V2 and node voltage V3, followed by nodal equations and a derived expression for V3 in blue ink.

$Handwritten algebra in blue ink solving a node-voltage equation, with some terms in red: v3 minus v1 over R1 equals i1, then v1 times bracketed fractions with R2R3, R1R3 and R1R2 in the denominators, minus v1 over R1, plus v2 times a bracketed fraction, continuing with further simplification steps.$

haruspex · Jan 19, 2015

You're not supposed to post working as handwritten images. It's hard to read and hard to reference when making comments.
Given the answer for a1, please post your working to obtain b1 in typed text - preferably LaTeX, or using subscripts, but that's not essential.

rude man · Jan 19, 2015

This is a good time to apply the superposition principle.

Node Method Problem: Identifying Errors

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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