Resistance in Parallel Equation

AI Thread Summary
The total resistance in a parallel circuit can be calculated using the formula 1/R=1/R1+1/R2+1/R3, but an alternative expression R=1/(1/R1+1/R2+1/R3) is also valid. The 1/R format is preferred for its simplicity and ease of memorization, as it clearly illustrates that voltage remains constant across all resistors. While some argue that the alternative equation is less common, it is still utilized, particularly in educational contexts where students are expected to manipulate equations. The discussion draws parallels to Newton's second law, emphasizing that both forms of the resistance equation are mathematically equivalent. Ultimately, the choice of expression often depends on the context and the user's familiarity with the equations.
CheesyPeeps
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The formula to find the total resistance in a parallel circuit is 1/R=1/R1+1/R2+1/R3, but wouldn't it be easier to use R=1/(1/R1+1/R2+1/R3)? I've only ever seen the equation written like that once before, and I'm wondering if there's a reason as to why it's never really used?
 
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What's easier to use depends on what you have and where you want to go.
The 1/R expression is easier to understand and to remember:

Voltage is the same for all R
Total current = Voltage / Total resistance
Total current = Sum of individual currents = Sum ( Voltage / Individual resistance i )​

Divide by Voltage and you get the 1/R = Sum (1/Ri )
 
CheesyPeeps said:
I'm wondering if there's a reason as to why it's never really used?
It is USED plenty. Students are expected to be able to divide easily.

Similarly, Newton's 2nd law is almost always written F=ma, even though students are expected to recognize and use the equivalent a=F/m and m=F/a.
 
Thanks! I suppose it does make sense that we don't write it that way.
 
What others said. The two equations are mathematically the same. If anything the second form of the equation is used more frequently.
 
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