(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Say I have a circuit that splits into three parallel wires. They each have a resistors on them of 2, 3, and 4 ohms respectively. They reconnect and their final current is 10 Amps. Is there a more intuitive way to find the current on each wire based on the ratios of ohms, rather than finding the voltage and using that to find the individual currents?

I know if the there were two parallel wires with resistors one each, I could sum the two R's together and use that as a denominator and the resistor of one wire as the numerator and multiply this fraction with the final current to find the current in the opposite wire. I want to know if this would work on more than 2 parallel wires and how. If it can, could somebody please explain using the example above.

2. Relevant equations

The sum of the currents from each wire should equal the final current after they are reconnected.

Voltage is same across parallel resistors.

Sum of R (parallel): R^{-1}= ((1/R_{1}) + (1/R_{2})...)

V=IR

3. The attempt at a solution

Sum R = 0.923 ohms

V = (10A)(0.923ohms) = 9.23V

I_{1}= (9.23V)/(2ohms) = 4.615A

I_{2}= (9.23V)/(3ohms) = 3.077A

I_{3}= (9.23V)/(4ohms) = 2.308A

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# Homework Help: Kirchhoff's Laws

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