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Ancient Geek · 17th May 2018, 12:53 pm

OK, I'll bite...

Measurements were:

Across R8: 926K
Across R9: 770K
Across R10: 443K

Let the three resistors of the star be Ra Rb and Rc.

Ra+Rb = 926K (Eq1)
Ra+Rc = 770K (Eq2)
Rb+Rc = 443K (Eq3)

Rearranging Eq3 we have:

Rb = 443K - Rc

Substituting for Rb in Eq1 we have:

Ra + 443K - Rc = 926K

Simplifying:

Ra - Rc = 483K

Adding this to Eq2 we have:

2 Ra + Rc - Rc = 483K + 770K

so:

Ra = 626.5K

Therefore Rb = 299.5K and Rc = 143.5K.

Now for the star to delta conversion...

Let Z be (Ra x Rb) + (Ra x Rc) + (Rb x Rc)

Z = 320517.75 x 10^9

R8 = Z / Rc ~= 2233.6K
R9 = Z / Rb ~= 1070.2K
R10 = Z / Ra ~= 511.6K

QED (quite easily done

)

17th May 2018, 12:53 pm	#12
Ancient Geek Retired Dormant Member Join Date: Aug 2017 Location: Bristol, UK. Posts: 136	Re: Resistor puzzle OK, I'll bite... Measurements were: Across R8: 926K Across R9: 770K Across R10: 443K Let the three resistors of the star be Ra Rb and Rc. Ra+Rb = 926K (Eq1) Ra+Rc = 770K (Eq2) Rb+Rc = 443K (Eq3) Rearranging Eq3 we have: Rb = 443K - Rc Substituting for Rb in Eq1 we have: Ra + 443K - Rc = 926K Simplifying: Ra - Rc = 483K Adding this to Eq2 we have: 2 Ra + Rc - Rc = 483K + 770K so: Ra = 626.5K Therefore Rb = 299.5K and Rc = 143.5K. Now for the star to delta conversion... Let Z be (Ra x Rb) + (Ra x Rc) + (Rb x Rc) Z = 320517.75 x 10^9 R8 = Z / Rc ~= 2233.6K R9 = Z / Rb ~= 1070.2K R10 = Z / Ra ~= 511.6K QED (quite easily done )