The equivalent resistance of three resistances of 10, 25, and 50 ? connected in parallel is _____ ?

The equivalent resistance of three resistances of 10, 25, and 50 ? connected in parallel is _____ ?

• A. 0.16
• B. 6.25
• C. 18.75
• D. 8.5

Answer: (B)

To determine the equivalent resistance \( R_{eq} \) of three resistors connected in parallel, you can use the formula: \[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \] In this case, the values of the resistors are 10 Ω, 25 Ω, and 50 Ω. Plugging these values into the formula gives: \[ \frac{1}{R_{eq}} = \frac{1}{10} + \frac{1}{25} + \frac{1}{50} \] Calculating each term separately: - For the 10 Ω resistor, \( \frac{1}{10} = 0.1 \) - For the 25 Ω resistor, \( \frac{1}{25} = 0.04 \) - For the 50 Ω resistor, \( \frac{1}{50} = 0.02 \) Adding these values together: \[ \frac{1}{R_{eq}} = 0.1 + 0.04 + 0.02 = 0.16

To determine the equivalent resistance ( R_{eq} ) of three resistors connected in parallel, you can use the formula:

[

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

]

In this case, the values of the resistors are 10 Ω, 25 Ω, and 50 Ω. Plugging these values into the formula gives:

[

\frac{1}{R_{eq}} = \frac{1}{10} + \frac{1}{25} + \frac{1}{50}

]

Calculating each term separately:

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

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

• For the 50 Ω resistor, ( \frac{1}{50} = 0.02 )

Adding these values together:

[

\frac{1}{R_{eq}} = 0.1 + 0.04 + 0.02 = 0.16