differentiate mathematically, between resistances in series and in parrallel
Hope this will give you a kick-start.
http://en.wikipedia.org/wiki/Series_and_parallel_circuits
http://www.kpsec.freeuk.com/resistan.htm
There is a lot of material you can obtain to help you complete your article.
Try Googling:
"resistance parallel series"
or other keywords.
If R1 and R2 be the two resistances connected in
(a)series, then equivalent resistance=R1+R2
(b)parallel, then equivalent resistance=(R1*R2)/(R1+R2)
To mathematically differentiate between resistances in series and in parallel, we need to understand how these two configurations are connected. Here's how you can differentiate them mathematically:
1. Resistances in Series:
When resistors are connected in series, their resistances add up to a total resistance. Mathematically, the total resistance (R_total) can be found by summing the individual resistances (R1, R2, R3, ...):
R_total = R1 + R2 + R3 + ...
So, the formula for calculating the total resistance for resistors in series is simply the sum of the individual resistances.
2. Resistances in Parallel:
When resistors are connected in parallel, the total resistance is given by the reciprocal of the sum of the reciprocals of the individual resistances. Mathematically, the formula is as follows:
1/R_total = 1/R1 + 1/R2 + 1/R3 + ...
So, to find the total resistance for resistors in parallel, you take the reciprocal of each resistance, sum them up, and then take the reciprocal of the sum.
In summary:
- For resistors in series, the total resistance is the sum of the individual resistances.
- For resistors in parallel, the total resistance is the reciprocal of the sum of the reciprocals of the individual resistances.