What is the total resistance if three resistances of 4 ohms, 6 ohms and 8 ohms respectively are connected in parallel?

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what is the total resistance if three resistances of 4 ohms, 6 ohms and 8 ohms respectively are connected in parallel?

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What is the total resistance if three resistances of 4 ohms, 6 ohms and 8 ohms respectively are connected in parallel?

Answer:
When resistors are connected in parallel, the total resistance (R_{total}) can be found using the reciprocal formula. The formula for the total resistance R_{total} of resistors R_1, R_2, and R_3 connected in parallel is given by:

\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}

Given:

  • R_1 = 4 \, \Omega
  • R_2 = 6 \, \Omega
  • R_3 = 8 \, \Omega

Let’s calculate the total resistance step by step:

  1. Calculate the reciprocals of each resistance:

    \frac{1}{R_1} = \frac{1}{4} \, \Omega^{-1} = 0.25 \, \Omega^{-1}
    \frac{1}{R_2} = \frac{1}{6} \, \Omega^{-1} \approx 0.1667 \, \Omega^{-1}
    \frac{1}{R_3} = \frac{1}{8} \, \Omega^{-1} = 0.125 \, \Omega^{-1}

  2. Sum the reciprocals:

    \frac{1}{R_{total}} = 0.25 + 0.1667 + 0.125
    \frac{1}{R_{total}} = 0.5417 \, \Omega^{-1}

  3. Find the total resistance by taking the reciprocal of the sum:

    R_{total} = \frac{1}{0.5417} \, \Omega \approx 1.846 \, \Omega

Final Answer:
The total resistance when three resistances of 4 ohms, 6 ohms, and 8 ohms are connected in parallel is approximately \boxed{1.846 \, \Omega}.

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