What is the total resistance of 10Ω, 20Ω, and 25Ω resistors connected in parallel?

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To find the total resistance of resistors connected in parallel, you use the formula for total resistance, ( R_t ), which is given by:

[

\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}

]

In this instance, the resistors are 10Ω, 20Ω, and 25Ω. Applying the formula will look as follows:

  1. First, calculate the reciprocals of each resistance:

  • For the 10Ω resistor: ( \frac{1}{10} = 0.1 )

  • For the 20Ω resistor: ( \frac{1}{20} = 0.05 )

  • For the 25Ω resistor: ( \frac{1}{25} = 0.04 )

  1. Next, sum the reciprocals:

[

\frac{1}{R_t} = 0.1 + 0.05 + 0.04 = 0.19

]

  1. Now, take the reciprocal of 0.19 to find the total resistance:

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