A 6-ω resistor, an 8-ω resistor, and a 24-ω resistor are connected together. what is the minimum resistance that can be produced using all three resistors?

Serie. In this configuration the current has only one path and the equivalent resistance is equal to the sum of all the resistances

[tex]R_{eq}= \sum R_i[/tex]

Parallel. This configuration the current has several paths, the equivalent resistances given by the expression

[tex]\frac{1}{R_{eq}} = \sum \frac{1}{R_i}[/tex]

They ask for the lowest value configuration, when examining the two configuration forms, the parallel configuration is the one that gives the lowest equivalent resistance

Indicate R₁= 6 Ω, R₂ = 8 Ω and R₃=12 Ω, in the attachment we can see a configuration of three resistors in parallel

Let's calculate

.[tex]\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}[/tex]

[tex]\frac{1}{R_{eq}} = \frac{1}{6} + \frac{1}{8} + \frac{1}{12}[/tex]

[tex]\frac{1}{R_{eq}} = 0.375[/tex]

[tex]R_{eq}[/tex] = 2.67 Ω

In conclusion, using the characteristics of series and parallel circuits we can find the results of the configuration of minimum resistance is:

Parallel circuit with equivalent resistance is 2.67 Ω

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