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AfilCa [17]
3 years ago
14

Solve for R1. Thank you! :)

Mathematics
2 answers:
lys-0071 [83]3 years ago
6 0

Answer:

\displaystyle R_1 = \frac{R_T\cdot R_2}{R_2 - R_T}

Step-by-step explanation:

We are given the equation:

\displaystyle \frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2}

And we want to solve for R₁.

We can multiply everything by the three denominators to remove all fractions:

\displaystyle R_TR_1R_2\left(\displaystyle \frac{1}{R_T}\right) = R_TR_1R_2\left(\frac{1}{R_1} + \frac{1}{R_2}\right)

Multiply:

\displaystyle R_1R_2 = R_TR_2 + R_TR_1

Isolate R₁:

\displaystyle R_1R_2 - R_1R_T = R_TR_2

We can factor:

\displaystyle R_1(R_2 - R_T) = R_TR_2

And divide. Therefore, in conclusion:

\displaystyle R_1 = \frac{R_T\cdot R_2}{R_2 - R_T}

nekit [7.7K]3 years ago
3 0

Answer:

\displaystyle \rm    R _{1} = \frac{ R _{T}R _{2} }{R _{2} - R _{T}}

Step-by-step explanation:

Just an alternative.

we would like to solve the following equation for {R_1}.

\displaystyle \rm  \frac{1}{R _{T} }  = \frac{1}{R _{1} }  +  \frac{1}{R _{2} }

in order to do so,we can simplify the right hand side which yields:

\displaystyle \rm  \frac{1}{R _{T} }  = \frac{R _{2} +  R _{1} }{R _{1} R _{2} }

<u>Steps</u><u>,</u><u> used</u><u> to</u><u> </u><u>simplify</u><u> the</u><u> </u><u>right</u><u> </u><u>hand</u><u> </u><u>side:</u>

  1. find the LCM of the denominators of the fractions i.e LCM(R_1,R_2)=R_1•R_2
  2. divide the LCM by the denominator of every fraction
  3. multiply the result of the division by the numerator of every fraction

Cross multiplication:

\displaystyle \rm  R _{1} R _{2}= R _{T}(R _{2} +  R _{1} )

distribute:

\displaystyle \rm  R _{1} R _{2}= R _{T}R _{2} + R _{T} R _{1}

isolate R_1 to the left hand side and change its sign:

\displaystyle \rm  R _{1} R _{2} - R _{T}R _{1}= R _{T}R _{2}

factor out R_1 from the left hand side expression:

\displaystyle \rm  R _{1} (R _{2} - R _{T})= R _{T}R _{2}

divide both sides by R_2-R_T:

\displaystyle \rm   \frac{R _{1} (R _{2} - R _{T})}{(R _{2} - R _{T})}= \frac{ R _{T}R _{2} }{(R _{2} - R _{T})}

reduce fraction:

\displaystyle \rm  \boxed{  R _{1} = \frac{ R _{T}R _{2} }{R _{2} - R _{T}}}

and we're done!

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