If three resistors of 12 ohms, 5 ohms, and 1 ohm are connected in parallel, what will be the combined resistance?

If three resistors of 12 ohms, 5 ohms, and 1 ohm are connected in parallel, what will be the combined resistance?

• A. More than 12 ohms
• B. 12 ohms
• C. Equal to 5 ohms
• D. Less than 1 ohm

Answer: (D)

When resistors are connected in parallel, the total or combined resistance decreases and is given by the formula: \[ \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \] In this case, the resistors are 12 ohms, 5 ohms, and 1 ohm. Applying the formula results in: \[ \frac{1}{R_{total}} = \frac{1}{12} + \frac{1}{5} + \frac{1}{1} \] Calculating the individual fractions: - \( \frac{1}{12} \) approximately equals 0.0833 - \( \frac{1}{5} \) equals 0.2 - \( \frac{1}{1} \) equals 1 Now, adding these fractions together: \[ 0.0833 + 0.2 + 1 = 1.2833 \] To find \( R_{total} \), take the reciprocal: \[ R_{total} = \frac{1}{1.2833} \approx 0.778

When resistors are connected in parallel, the total or combined resistance decreases and is given by the formula:

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

In this case, the resistors are 12 ohms, 5 ohms, and 1 ohm. Applying the formula results in:

[ \frac{1}{R_{total}} = \frac{1}{12} + \frac{1}{5} + \frac{1}{1} ]

Calculating the individual fractions:

• ( \frac{1}{12} ) approximately equals 0.0833

• ( \frac{1}{5} ) equals 0.2

• ( \frac{1}{1} ) equals 1

Now, adding these fractions together:

[ 0.0833 + 0.2 + 1 = 1.2833 ]

To find ( R_{total} ), take the reciprocal:

[ R_{total} = \frac{1}{1.2833} \approx 0.778