Proof of Relationship in Parallel Circuit Using Kirchoff's Law

AI Thread Summary
The discussion focuses on proving the relationship between the equivalent resistance of a parallel circuit and its constituent resistors using Kirchhoff's Law. It establishes that the total current in a parallel circuit is the sum of the individual currents through each resistor. Since the voltage across each resistor remains constant, the equation V/R_total = V/R1 + V/R2 + V/R3 simplifies to 1/R_total = 1/R1 + 1/R2 + 1/R3. This confirms the mathematical relationship between equivalent resistance and individual resistances in parallel circuits. The explanation is validated as correct.
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Homework Statement

How do I prove the relationship between the equivalent resistance of a parallel circuit and the values of the constituent resistors exist?



Homework Equations


V=IR


The Attempt at a Solution



Is it because:

I total= I1+I2+I3

and V is the same in parallel so.

V/R total= V/R1 + V/R2 + V/R3

and divide by V so

1/R= 1/R1 + 1/R2 + 1/R3.

is that why?
 
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That's exactly why. Well done.
 

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