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JRE
JRE
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Ohm's Lawlaw paradox?

Ohm = surname, ohm = unit
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winny
winny
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I have a chain of 4 single resistors in series. Call them R1, R2, R3, R4. When I measure the total resistance from top to bottom, then I get the same result as if I measure each pair of resistors: (R1+R2) + (R3+R4). I usually get the same result if I measure the resistors this way: R1 + (R2+R3) + R4.

I say "usually" because if I now install a jumper between the top of R1 and the bottom of R2, then the results are not the same. Measuring R1 now gives the value equal to R1 in parallel with R2, making the sum of the measurements equal to more than the total resistance measured from top to bottom.

If for example each resistor is 1 kOhmkohm, then the total resistance with R1 and R2 jumpered is 2kOHm2 kohm. But if I measure R1 + (R2+R3) + R4, then the total is 3 kOhm.

This is based on a real-life situation where we can only easily measure the junction between resistors R1 and R2, the junction between R3 and R4, etc. And we can't measure the total resistance at once, because it is thousands of megohms. Is there some way to mathematically extract the correct total resistance from this type of measurement?

I have a chain of 4 single resistors in series. Call them R1, R2, R3, R4. When I measure the total resistance from top to bottom, then I get the same result as if I measure each pair of resistors: (R1+R2) + (R3+R4). I usually get the same result if I measure the resistors this way: R1 + (R2+R3) + R4.

I say "usually" because if I now install a jumper between the top of R1 and the bottom of R2, then the results are not the same. Measuring R1 now gives the value equal to R1 in parallel with R2, making the sum of the measurements equal to more than the total resistance measured from top to bottom.

If for example each resistor is 1 kOhm, then the total resistance with R1 and R2 jumpered is 2kOHm. But if I measure R1 + (R2+R3) + R4, then the total is 3 kOhm.

This is based on a real-life situation where we can only easily measure the junction between resistors R1 and R2, the junction between R3 and R4, etc. And we can't measure the total resistance at once, because it is thousands of megohms. Is there some way to mathematically extract the correct total resistance from this type of measurement?

I have a chain of 4 single resistors in series. Call them R1, R2, R3, R4. When I measure the total resistance from top to bottom, then I get the same result as if I measure each pair of resistors: (R1+R2) + (R3+R4). I usually get the same result if I measure the resistors this way: R1 + (R2+R3) + R4.

I say "usually" because if I now install a jumper between the top of R1 and the bottom of R2, then the results are not the same. Measuring R1 now gives the value equal to R1 in parallel with R2, making the sum of the measurements equal to more than the total resistance measured from top to bottom.

If for example each resistor is 1 kohm, then the total resistance with R1 and R2 jumpered is 2 kohm. But if I measure R1 + (R2+R3) + R4, then the total is 3 kOhm.

This is based on a real-life situation where we can only easily measure the junction between resistors R1 and R2, the junction between R3 and R4, etc. And we can't measure the total resistance at once, because it is thousands of megohms. Is there some way to mathematically extract the correct total resistance from this type of measurement?

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theber
theber
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Ohm's Law paradox?

I have a chain of 4 single resistors in series. Call them R1, R2, R3, R4. When I measure the total resistance from top to bottom, then I get the same result as if I measure each pair of resistors: (R1+R2) + (R3+R4). I usually get the same result if I measure the resistors this way: R1 + (R2+R3) + R4.

I say "usually" because if I now install a jumper between the top of R1 and the bottom of R2, then the results are not the same. Measuring R1 now gives the value equal to R1 in parallel with R2, making the sum of the measurements equal to more than the total resistance measured from top to bottom.

If for example each resistor is 1 kOhm, then the total resistance with R1 and R2 jumpered is 2kOHm. But if I measure R1 + (R2+R3) + R4, then the total is 3 kOhm.

This is based on a real-life situation where we can only easily measure the junction between resistors R1 and R2, the junction between R3 and R4, etc. And we can't measure the total resistance at once, because it is thousands of megohms. Is there some way to mathematically extract the correct total resistance from this type of measurement?