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$The resistance of a circuit formed by connecting two resistors in parallel is given by (1)/((1)/(R_(1))+(1)/(R_(2))). Find the resistance of the circuit if R_(1)=8 and R_(2)=12. The solution is a fraction whose numerator is and whose denominator is$

The resistance of a circuit formed by connecting two resistors in parallel is given by $\newline$ $\frac{1}{\frac{1}{R_{1}}+\frac{1}{R_{2}}} .$ $\newline$ Find the resistance of the circuit if $R_{1}=8$ and $R_{2}=12$ . The solution is a fraction whose numerator is $\newline$ and whose denominator is

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Q. The resistance of a circuit formed by connecting two resistors in parallel is given by

\newline

\frac{1}{\frac{1}{R_{1}}+\frac{1}{R_{2}}} .

\newline

Find the resistance of the circuit if

R_{1}=8

and

R_{2}=12

. The solution is a fraction whose numerator is

\newline

and whose denominator is

Write Formula: Write down the formula for the total resistance ( $R_T$ ) of two resistors connected in parallel. $\newline$ The formula is: $\newline$ $\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2}$
Substitute Values: Substitute the given values of $R_1$ and $R_2$ into the formula. $\newline$ $R_1 = 8 \, \text{ohms}, R_2 = 12 \, \text{ohms},$ so: $\newline$ $\frac{1}{R_T} = \frac{1}{8} + \frac{1}{12}$
Find Common Denominator: Find a common denominator for the fractions on the right-hand side of the equation. $\newline$ The common denominator for $8$ and $12$ is $24$ . $\newline$ $\frac{1}{R_T} = \frac{3}{24} + \frac{2}{24}$
Add Fractions: Add the fractions on the right-hand side of the equation. $\newline$ $\frac{1}{R_T} = \frac{3}{24} + \frac{2}{24} = \frac{5}{24}$
Take Reciprocal: Take the reciprocal of both sides of the equation to solve for $R_T$ . $\newline$ $R_T = \frac{24}{5}$