Current Divider Formula if R for element = 0

[cavalieregi]

Hi I was wondering say for example you had this simple current divider circuit.

I was wondering if R₁ for example had zero resistance it would have all current dropped over it. However pertaining to the current divider formula.

$I_i = Is (R_T / R_i)$

Thus if R₁ = zero the equation is not defined but that also means R₂ = R_T and the equation would claim all current would be dropped over R₂?

 

[Nugatory]

If R1 were zero then it would be a wire not a resistor, so in effect the two terminals of the voltage source would be connected directly to one another forming a short circuit. Try building this circuit and either a fuse will blow or something will break, catch on fire, or explode.

To properly analyze these situations, you have to recognize that zero resistance is an idealization that doesn't exist in the real world. Instead you must use the very small but non-zero resistance that any real wire has. When you do, you will see that the total current is very large while the current across R2 is near zero.

 

[nasu]

Where did you get that formula from? It does not seem to apply here. You should have the sum of the two resistances in the denominator.

 

[cavalieregi]

Where did you get that formula from? It does not seem to apply here. You should have the sum of the two resistances in the denominator.

Yes I just realized sorry. Now It makes sense.

 

[sardar]

I would like to clarify that the current divider formula is used to calculate the current flowing through a specific resistor in a circuit. It takes into account the total resistance of the circuit and the individual resistance of the resistor in question. In the scenario you have described, if R1 has a resistance of zero, it would essentially act as a short circuit, meaning that all the current would flow through R1 and none through R2. This is because the current will always follow the path of least resistance. Therefore, the current divider formula would not be applicable in this situation. It is important to note that in real-world circuits, it is not possible to have a resistor with zero resistance.