Combining Ohm's Laws Formulas
Date: 04/12/2001 at 16:41:14 From: Tony Subject: Algebraic formulas I'm studying math for electronics, and we have two main formulas: V = IR and P = VI. My problem is to combine them to get one formula. I understand how to make one formula by dividing both sides by the same letter, like I = P/V, but I just can't grasp the idea of combining these separate formulas to make one. Is there an easy way to figure this out? Can you help me please? Thanks, Dr. Math.
Date: 04/13/2001 at 13:09:32 From: Doctor TWE Subject: Re: Algebraic formulas Hi Tony - thanks for writing to Dr. Math. The formulas E = I*R and P = I*E are called Ohm's laws, named after the person who first defined the relations, Georg Ohm. As you stated, we can divide each side of either equation by the same thing to solve for another value. Doing this, we get: E = I*R and P = I*E I = E/R I = P/E R = E/I E = P/I The formulas on the left relate the values of voltage, current, and resistance, while the formulas on the right relate the values of power, current, and voltage. There are six more forms of Ohm's laws; three that relate power, current, and resistance; and three that relate power, voltage, and resistance. To get those formulas, we have to combine the two basic formulas above. The easiest way to do that is to use substitution. Let's start with Ohm's power law, P = I*E. Now we know from Ohm's voltage law that E = I*R, so we'll substitute I*R into the first equation: P = I*E ^ (I*R) P = I*(I*R) See how I just took E out of the equation and replaced it with (I*R)? Now I can use the rules of algebra to simplify: P = I*(I*R) = I*I*R = I^2*R So our first "new" equation is P = I^2*R. I can then solve that equation for I and R to get 2 more formulas: P = I^2*R and P = I^2*R P I^2*R P I^2*R --- = ----- --- = ----- I^2 I^2 R R R = P/I^2 I^2 = P/R I = sqrt(P/R) So now we have the formulas R = P/I^2 and I = sqrt(P/R) as well. Now go back to Ohm's power law, P = I*E. This time, substitute for I (using the form of Ohm's voltage law that states I = E/R). Replace I in the first equation with (E/R) and simplify. You'll have an equation with just P, E and R. You can then solve that equation for each of the three variables to get three more formulas. I'll leave that for you to do. When you are finished, you'll have twelve formulas; three each of the forms: E = ... I = ... R = ... and P = ... Then, given any two quantities, you can solve for the desired one. For more on the substitution method, check out the following entries from our Ask Dr. Math archives: Solving Systems of Equations by Substitution http://mathforum.org/dr.math/problems/lynn8.24.98.html System of Equations and the Substitution Method http://mathforum.org/dr.math/problems/poindexter6.7.98.html Solving Pairs of Equations by Substitution http://mathforum.org/dr.math/problems/lana11.26.97.html I hope this helps. If you have any more questions, write back. - Doctor TWE, The Math Forum http://mathforum.org/dr.math/
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