No Current, No Voltage?

Hexspa

Joined Jul 3, 2023
7
Hi, first post. This is a question I put under the Voltage, Current, and Resistance Worksheet ( https://www.allaboutcircuits.com/worksheets/voltage-current-and-resistance/ ) but I think this forum might answer faster:

I can understand that voltage is potential energy to move an electron between two points and that something like a battery stores this potential independently of current flow. However, if Ohm’s Law states that V=IR and anything multiplied by zero is zero then V=0x has to be V=0. No current, no voltage. How to reconcile this seeming paradox?

WBahn

Joined Mar 31, 2012
30,068
Hi, first post. This is a question I put under the Voltage, Current, and Resistance Worksheet ( https://www.allaboutcircuits.com/worksheets/voltage-current-and-resistance/ ) but I think this forum might answer faster:

I can understand that voltage is potential energy to move an electron between two points and that something like a battery stores this potential independently of current flow. However, if Ohm’s Law states that V=IR and anything multiplied by zero is zero then V=0x has to be V=0. No current, no voltage. How to reconcile this seeming paradox?
No paradox -- Ohm's Law applies to resistors and a battery is not a resistor.

Ohm's Law says that the voltage ACROSS a resistor is equal to the product of the resistance and the current THROUGH the resistor.

So for an unconnected battery, the resistance that the 12 V is across is infinite and there is zero current.

I = V/R = 12 V / oo Ω = 0 A

For

V = I·R

You have (0 A)( oo Ω) which, mathematically, is what is known as an "indeterminant form", meaning that it could be anything. In this case, it's 12 V.

nsaspook

Joined Aug 27, 2009
13,305
Hi, first post. This is a question I put under the Voltage, Current, and Resistance Worksheet ( https://www.allaboutcircuits.com/worksheets/voltage-current-and-resistance/ ) but I think this forum might answer faster:

I can understand that voltage is potential energy to move an electron between two points and that something like a battery stores this potential independently of current flow. However, if Ohm’s Law states that V=IR and anything multiplied by zero is zero then V=0x has to be V=0. No current, no voltage. How to reconcile this seeming paradox?

MrChips

Joined Oct 2, 2009
30,821
I way I like to state it, Ohm's Law is:

I = V / R

If R = ∞, I = 0

Hexspa

Joined Jul 3, 2023
7
No paradox -- Ohm's Law applies to resistors and a battery is not a resistor.

Ohm's Law says that the voltage ACROSS a resistor is equal to the product of the resistance and the current THROUGH the resistor.

So for an unconnected battery, the resistance that the 12 V is across is infinite and there is zero current.

I = V/R = 12 V / oo Ω = 0 A

For

V = I·R

You have (0 A)( oo Ω) which, mathematically, is what is known as an "indeterminant form", meaning that it could be anything. In this case, it's 12 V.
I see my mistake which is I didn’t account for the resistance value. Even if I had, I’ve never heard of indeterminate forms. Nsaspook’s link took me into limit theory which, while I’ve heard of such concepts from audio dynamic range compressors, I’m a long way from grasping the math. Thanks for your help.