EBF 483
Introduction to Electricity Markets

2.2.2 Parallel Resistance

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The figure below shows two elements connected in parallel.

Enter image and alt text here. No sizes!
Figure 2.5: Enter caption here
Source: Seth Blumsack
  • One element has resistance R1
  • The other element has resistance R2
  • The equivalent parallel resistance between A and B is:

1 R AB = 1 R 1 + 1 R 2

This is a different-looking rule than for series resistances. We say that parallel resistances are "inversely additive." To calculate the equivalent resistance for elements in parallel, you would first take the inverse of each individual resistance, add those up, and take the inverse of the sum.

Here is an example of how this works. Let's plug some numbers into the parallel elements figure.

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Figure 2.6: Enter caption here
Source: Seth Blumsack

How can we calculate the equivalent parallel resistance here? Let's dive in and use our equation directly:

1 R AB  =  1 10  +  1 20          =  2 20  +  1 20          =  3 20

Since 1 R AB = 3 20 we would have an equivalent parallel resistance in this system of R AB = 20/ .

Here is another example that you can try yourself. If R1 = 5 Ω and R2 = 7 Ω in the parallel system figure above, show that the equivalent parallel resistance is 35/12 Ω.