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

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

• A. 5.26Ω
• B. 5.5Ω
• C. 9.25Ω
• D. 10.52Ω

Answer: (A)

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: \( \frac{1}{25} = 0.04 \) 2. Next, sum the reciprocals: \[ \frac{1}{R_t} = 0.1 + 0.05 + 0.04 = 0.19 \] 3. Now, take the reciprocal of 0.19 to find the total resistance: \

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 )

2. Next, sum the reciprocals:

[

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

]

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

\