the formula 1/R = 1/R1 + 1/R2, concerning resistance in an electrical circuit is used in physics. if R = 3 ohms and R1 is 8 ohms more than R2, the value of R1 be?
this also not make any sense to me
R2 = R1 - 8
R1 R2 = R R2 + R R1 = R(R1+R2)
R1(R1-8) = 3(2 R1 - 8)
R1^2 - 8 R1 = 6 R1 - 24
R1^2 -14 R1 + 24 = 0
(R1-12)(R1-2) = 0
If R1 were 2, R2 would be negative, no good
so
R1 = 12 (and R2 is 4)
that make sense now :) thanks very much damon :)
The formula 1/R = 1/R1 + 1/R2, known as the formula for resistors in parallel, is used in physics to calculate the total resistance of a circuit when multiple resistors are connected in parallel.
To find the value of R1 when R = 3 ohms and R1 is 8 ohms more than R2, we can use the given equation.
First, let's substitute R = 3 ohms into the equation:
1/3 = 1/R1 + 1/R2
Now, let's use the information that R1 is 8 ohms more than R2. We can express this mathematically as:
R1 = R2 + 8
Substituting R1 and R2 + 8 into the equation, we have:
1/3 = 1/(R2 + 8) + 1/R2
Now, we need to solve this equation to find the value of R2. To simplify it, we can multiply both sides of the equation by 3R2(R2 + 8):
3R2(R2 + 8) * (1/3) = 3R2(R2 + 8) * (1/(R2 + 8) + 1/R2)
R2(R2 + 8) = 3(R2 + 8) + 3R2
Expanding and simplifying the equation:
R2^2 + 8R2 = 3R2 + 24 + 3R2
R2^2 + 8R2 = 6R2 + 24
R2^2 + 8R2 - 6R2 - 24 = 0
R2^2 + 2R2 - 24 = 0
Now, we can solve this quadratic equation to find the value(s) of R2 using factoring or the quadratic formula:
(R2 - 4)(R2 + 6) = 0
Solving each factor separately:
R2 - 4 = 0, which gives R2 = 4
R2 + 6 = 0, which gives R2 = -6 (we will ignore this negative result, as resistance cannot be negative)
Therefore, R2 = 4 ohms.
Now that we know R2, we can find R1 using the equation R1 = R2 + 8:
R1 = 4 + 8
R1 = 12 ohms.
So, the value of R1 is 12 ohms.