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I am struggling to see how an equation has been transposed. It is probably pretty easy, so apologies in advance.

If possible; please show the transposition stages:

$V_{out} = V1 . \frac{R2}{R1 + R2} (\frac{R3 + R4}{R3}) - V2 . \frac {R4} {R3}$

this is then transposed to.....

$V_{out} = (V1 - V2) \frac {R4} {R3}$

RGS
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martin
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  • Do you know any relations between the different $R_i$? – RGS Nov 15 '16 at 18:30
  • Hi. This equation comes from an engineering textbook to describe the operation of a component. The textbook states that R1 can be equivalent to R3 and that R2 can be equivalent to R4. – martin Nov 16 '16 at 10:48

1 Answers1

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Without further conditions relating $R_1, R_2, R_3, R_4$ to one another, these two equations are not equivalent.

EDIT: You say that $R_1 = R_3$ and $R_2 = R_4$. In that case,

\begin{align*} V_1 &\left(\frac{R_2}{R_1 + R_2}\right) \left(\frac{R_3 + R_4}{R_3}\right) - V_2 . \frac {R_4} {R_3} \\[3mm] &= V_1 \left(\frac{R_4}{R_3 + R_4}\right) \left(\frac{R_3 + R_4}{R_3}\right) - V_2 \frac {R_4} {R_3} \\[3mm] &= V1 \frac{R_4}{R_3} - V2 \frac {R_4} {R_3} = (V1 - V2) \frac{R_4}{R_3} \end{align*}

Daniel McLaury
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  • Hi. This equation comes from an engineering textbook to describe the operation of a component. The textbook states that R1 can be equivalent to R3 and that R2 can be equivalent to R4. – martin Nov 16 '16 at 10:48
  • Then change all the R1's to R3 and all the R2's to R4's in the equation. – Daniel McLaury Nov 16 '16 at 14:34
  • If you changed the R1s and R2s to R3s and R4s, why are there still R1s and R2s there? – Daniel McLaury Nov 17 '16 at 06:21
  • Hi Daniel; thanks for the advice. I did try that, but I still could not get to the answer. First I tried to multiply out the brackets in the first term: R2 / R1 + R2 (R3 + R4 / R3) by multiplying the numerators and the denominators to get R2R3 + R2R4 on the numerator, and R1R3 + R2R3 on the denominator. Next, I collected both V terms together to get 'V1 - V2'. I subtracted R2R3 + R2R4 \ R1R3 + R2R3 and R4 \ R3, but still could not get it – martin Nov 17 '16 at 06:40
  • Edited answer to respond. – Daniel McLaury Nov 17 '16 at 06:47