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3 years ago

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18. A circuit contains a 10 ohm resistor, a 50 ohm resistor, and an 80 ohm resistor connected in parallel. If you test this circ

uit with a DMM, you should read a total resistance value
A. 0.13 ohms
B. 75 ohms
C. 140 ohms
D. 7.55 ohms

1 answer:

lutik1710 [3]3 years ago

4 0

The equivalent resistance is D) $7.55 \Omega$

Explanation:

The equivalent resistance of n resistors in parallel is given by the equation:

$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+...+\frac{1}{R_n}$

For three resistors such as in this problem, the equation becomes

$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$

where we have the following:

$R_1 = 10 \Omega$ is the resistance of the 1st resistor

$R_2 = 50 \Omega$ is the resistance of the 2nd resistor

$R_3 = 80 \Omega$ is the resistance of the 3rd resistor

Substituting, we find the equivalent resistance:

$\frac{1}{R}=\frac{1}{10}+\frac{1}{50}+\frac{1}{80}=0.133 \Omega^{-1}$

$R=\frac{1}{0.133}=7.55 \Omega$

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