How can the literal equation 1/r1 + 1/r2 = 1/R be solved for R? Please help me.
well, that is the formula for the electrical resistance of r1 and r2 in parallel :)
multiply both sides by r1*r2*R
r2 R + r1 R = r1 r2
R ( r1+r2) = r1 r2
R = r1 r2 / (r1+r2)
another way to think about it is "conductance" = 1/resistance
C = c1 + c2 if in parallel
C = 1/r1 + 1/r2 = (r1 + r2)/r1 r2
1/C = R = r1 r2 / (r1 + r2)
Thank you Anonymous.
You are welcome.
1R=1R1+1R2+...1R=1R1+1R2+...
R=ρ⋅lAR=ρ⋅lA
can someone help me
To solve the literal equation 1/r1 + 1/r2 = 1/R for R, you need to isolate R on one side of the equation. Here's how you can do it:
Step 1: Start with the given equation: 1/r1 + 1/r2 = 1/R.
Step 2: Find a common denominator for the fractions on the left side of the equation. The common denominator is r1 * r2 * R.
Since r1 and r2 are already in the equation, we need to multiply the whole equation by R to get the denominator R * r1 * r2 for both fractions.
Multiplying the equation by R, we get: R/r1 + R/r2 = 1.
Step 3: Combine the fractions with a common denominator. The result is: (R*r2 + R*r1)/(r1*r2) = 1.
Step 4: Simplify the numerator by factoring out the R: R(r2 + r1)/(r1*r2) = 1.
Step 5: Multiply both sides by r1*r2 to get rid of the denominator: R(r2 + r1) = r1*r2.
Step 6: Distribute the R on the left side: R*r2 + R*r1 = r1*r2.
Step 7: Move the R*r2 term to the right side by subtracting it from both sides: R*r1 = r1*r2 - R*r2.
Step 8: Factor out R on the left side: R(r1) = r1*r2 - R*r2.
Step 9: Move the R*r2 term to the left side by adding it to both sides: R*r1 + R*r2 = r1*r2.
Step 10: Factor out R on the right side: R(r1 + r2) = r1*r2.
Step 11: Finally, divide both sides by (r1 + r2) to solve for R: R = (r1*r2) / (r1 + r2).
So, the solution to the equation 1/r1 + 1/r2 = 1/R for R is R = (r1*r2) / (r1 + r2).