How do i derive the formula for "E" in terms of P & R using the equations E= I x R & P= I x E

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violy's profile pic

violy | High School Teacher | (Level 1) Associate Educator

Posted on

Solve for I on P = I x E. 

Since, E is being multiplied on right side, we divide both sides by E. 

`(P/E) = (I x E)/E`

Cancel common factor on top and bottom of right side.

`P/E = I` or `I = P/E` 

Replace the I on E = I x R by what we got. 

`E = (P/E) x R`

Multiply both sides by E. 

`E x E = E x (P/E)x R` 

`E^(2) = P x R`

Take the square root of both sides. 

`E = sqrt(P x R)`

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pramodpandey's profile pic

pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on

Eliminate I from both equation (only I prsent in both equation)

since  `E=IxxR`

`E/R=I`                  (i)

also

`P=ExxI`

`P/E=I`                   (ii)

from (i) and (ii) ,we have

`E/R=P/E`

cross multiply

`E^2=PxxR`

which is required formula.

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