A parallel circuit contains an 18 ohm and a 9 ohm resistor. What is the total resistance?

A parallel circuit contains an 18 ohm and a 9 ohm resistor. What is the total resistance?

• A. 27 ohms
• B. 18 ohms
• C. 9 ohms
• D. 6 ohms

Answer: (D)

To find the total resistance of resistors connected in parallel, the formula used is: 1/R_total = 1/R1 + 1/R2 In this case, the resistors are 18 ohms and 9 ohms. Applying the values to the formula: 1/R_total = 1/18 + 1/9 To perform the addition, we first need to express both fractions with a common denominator. The least common multiple of 18 and 9 is 18. Thus, we can rewrite 1/9 as 2/18: 1/R_total = 1/18 + 2/18 1/R_total = 3/18 Next, simplify 3/18 to 1/6: 1/R_total = 1/6 Taking the reciprocal gives us the total resistance: R_total = 6 ohms This shows that in a parallel circuit, the total resistance decreases as more resistors are added, as opposed to a series circuit where resistance accumulates. Thus, the total resistance of the parallel circuit with an 18 ohm and a 9 ohm resistor is indeed 6 ohms, which is the correct answer.

To find the total resistance of resistors connected in parallel, the formula used is:

1/R_total = 1/R1 + 1/R2

In this case, the resistors are 18 ohms and 9 ohms. Applying the values to the formula:

1/R_total = 1/18 + 1/9

To perform the addition, we first need to express both fractions with a common denominator. The least common multiple of 18 and 9 is 18. Thus, we can rewrite 1/9 as 2/18:

1/R_total = 1/18 + 2/18

1/R_total = 3/18

Next, simplify 3/18 to 1/6:

1/R_total = 1/6

Taking the reciprocal gives us the total resistance:

R_total = 6 ohms

This shows that in a parallel circuit, the total resistance decreases as more resistors are added, as opposed to a series circuit where resistance accumulates. Thus, the total resistance of the parallel circuit with an 18 ohm and a 9 ohm resistor is indeed 6 ohms, which is the correct answer.