What is the total resistance in a parallel circuit with two resistances of 4 ohms and 6 ohms?

• A. 2.4 ohms
• B. 3.6 ohms
• C. 6 ohms
• D. 10 ohms

Answer: (A)

To find the total resistance in a parallel circuit with resistances of 4 ohms and 6 ohms, you can use the formula for total resistance (R_total) in parallel, which is given by:

[

\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2}

]

Substituting the values for R_1 and R_2:

[

\frac{1}{R_{total}} = \frac{1}{4} + \frac{1}{6}

]

To combine these fractions, you first find a common denominator, which in this case is 12. Now you rewrite the fractions:

[

\frac{1}{R_{total}} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}

]

Now, take the reciprocal to find R_total:

[

R_{total} = \frac{12}{5} = 2.4 \text{ ohms}

]

Thus, the total resistance of the parallel circuit with these two resistances is indeed 2.4 ohms. This reasoning shows how in parallel circuits,