Proof of Relationship in Parallel Circuit Using Kirchoff's Law

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SUMMARY

The relationship between the equivalent resistance of a parallel circuit and its constituent resistors is established through Kirchhoff's Law. In a parallel circuit, the total current (I total) is the sum of the individual currents (I1, I2, I3), while the voltage (V) remains constant across all resistors. This leads to the formula for equivalent resistance: 1/R total = 1/R1 + 1/R2 + 1/R3, confirming the mathematical relationship between the resistors.

PREREQUISITES
  • Understanding of Kirchhoff's Laws
  • Basic knowledge of Ohm's Law (V=IR)
  • Familiarity with parallel circuit configurations
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study Kirchhoff's Voltage and Current Laws in detail
  • Explore practical applications of parallel circuits in electronics
  • Learn about calculating equivalent resistance in complex circuits
  • Investigate the impact of resistor values on total current in parallel circuits
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Students studying electrical engineering, educators teaching circuit theory, and hobbyists interested in electronics and circuit design.

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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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