# Thread: Help slope calculation understanding

1. ## Help slope calculation understanding

Hi, I am new to this website, and learning a bit of math on my own, Need help on this slope calculation, I am looking to learn where the products are coming from in the equation. here is the question. Electrical differential slope calculation – ( w1 is winding 1 and w2 is winding 2 )
SLP1 (slope 1 = 20% or 0.2) IOP = (Iw1 - Iw2) IRT = (Iw1 + Iw2)/2
Equation solve à IOP=SLP1/100 x IRT
Step 1 -> IOP = 0.2/100 x IRT
Step 2 -> (Iw1 - Iw2) = 0.2 x (Iw1 + Iw2)/2
Step 3 -> 2 x (Iw1 - Iw2) = 0.2 x (Iw1 + Iw2)
Step 4 -> 2 x (Iw1 - Iw2)/0.2 = (Iw1 + Iw2)
Step 4 -> 10 x (Iw1 - Iw2) = (Iw1 + Iw2) -> question 1 -> where did the “10” come from?
Step 5 -> 10Iw1 – 10Iw2 = Iw1 +Iw2
Step 6 -> 10Iw1 – Iw1 = Iw2 + 10Iw2
Step 7 -> 9Iw1 = 11Iw2 -> question 2 -> I get that 10 -1 = 9 and 10 +1 = 11, but why . is this allowed?
Step 8 -> Iw1 = 11/9Iw2
Step 9 -> Iw1 = 1.222Iw2
Step 10 -> 9Iw1 = 11Iw2
Step 11 -> 9/11Iw1 = w2
Step 12 -> Iw2 = 0.818Iw1
Fin! With 2 questions This is for a relay application in per unit, but I am having trouble understanding the theory behind the process here. any help is apprecitated

2. ## Re: Help slope calculation understanding

Originally Posted by rumor84
...
Step 4 -> 2 x (Iw1 - Iw2)/0.2 = (Iw1 + Iw2)
Step 4 -> 10 x (Iw1 - Iw2) = (Iw1 + Iw2) -> question 1 -> where did the “10” come from?
step 4: $\frac{2 \cdot (I_{w_1}-I_{w_2})}{0.2} = ....$

and what value has $\frac2{0.2}$ ?

Step 5 -> 10Iw1 – 10Iw2 = Iw1 +Iw2
Step 6 -> 10Iw1 – Iw1 = Iw2 + 10Iw2
Step 7 -> 9Iw1 = 11Iw2 -> question 2 -> I get that 10 -1 = 9 and 10 +1 = 11, but why . is this allowed?
...
a) a more real life example: If you have 10 candies and eat one, how many candies are left?
b) a more formal attempt:

$10I_{w_1} = 10 \cdot I_{w_1}$

That means that you have in this line

$10I_{w_1} - I_{w_1}$

two summands with a common factor:

$10 \cdot I_{w_1} - 1 \cdot I_{w_1} = I_{w_1}(10-1) = 9I_{w_1}$

3. ## Re: Help slope calculation understanding

Ohhh, I see it now, and couldn't be more clear. thank you for the help!