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s344n2d4d5 [400]
3 years ago
12

If R is the total resistance for a parallel circuit with two resistors of resistances of r1 and r2 then 1/r=1/r1+1/r2 find the r

esistance r1 if the total resistance is 20 ohms and r2 is 75 ohms round your answer to the nearest ohms if neccesary
a.16 ohms
b.1405 ohms
c.27 ohms
d.102 ohms
Mathematics
2 answers:
Allushta [10]3 years ago
6 0
A little Algebra, and we're home free!

We are given R = 20 and r2 = 75. We need to find r1.

The formula is 1/R = 1/r1 + 1/r2. Plug-in:
1/20 = 1/r1 + 1/75
1/20 - 1/75 = 1/r1
0.0366 = 1/r1
r1 = 1/0.03666
r1 = 27.272

Our answer is r1 = 27 ohms.
nikitadnepr [17]3 years ago
3 0

Answer:

The correct answer is c. 27\Omega

Step-by-step explanation:

- The first step is to get the r_1 variable for alone on one side.

\frac{1}{r}=\frac{1}{r_1}+\frac{1}{r_2}

  • Pass the term \frac{1}{r_2} to subtract to the left side.

\frac{1}{r}-\frac{1}{r_2}=\frac{1}{r_1}

  • Pass the term \frac{1}{r}-\frac{1}{r_2} to divide to the right side and pass the term r_1 to multiply to the left side.

r_1=\frac{1}{\frac{1}{r}-\frac{1}{r_2}}

- The second step is to replace the values of r and r_2 into the previous expression.

r_1=\frac{1}{\frac{1}{20}-\frac{1}{75}}

- The third step is to perform the operations to simplify the expression.

r_1=\frac{1}{0.05-0.01333}

r_1=\frac{1}{0.03666}

r_1=27.2727\Omega

As it is necessary to round the answer, the value of r_1 is 27\Omega.

Thus, the correct answer is c. 27\Omega

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