The equivalent resistance is D) [tex]7.55 \Omega[/tex]
Explanation:
The equivalent resistance of n resistors in parallel is given by the equation:
[tex]\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+...+\frac{1}{R_n}[/tex]
For three resistors such as in this problem, the equation becomes
[tex]\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}[/tex]
where we have the following:
[tex]R_1 = 10 \Omega[/tex] is the resistance of the 1st resistor
[tex]R_2 = 50 \Omega[/tex] is the resistance of the 2nd resistor
[tex]R_3 = 80 \Omega[/tex] is the resistance of the 3rd resistor
Substituting, we find the equivalent resistance:
[tex]\frac{1}{R}=\frac{1}{10}+\frac{1}{50}+\frac{1}{80}=0.133 \Omega^{-1}[/tex]
[tex]R=\frac{1}{0.133}=7.55 \Omega[/tex]
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