Question

A circuit has 3 resistors, all connected in parallel. Let R1 = 4.0 Ω, R2 = 3.0 Ω, and R3 = 6.0 Ω. What is the equivalent resistance of the circuit? Show all work and include units of measure.

Answer 1

The effective resistance is the reciprocal of

1/4 + 1/3 + 1/6 =

3/12 + 4/12 + 2/12 =

9/12 Siemens

The reciprocal is 12/9 ohms.

That's 4/3 or 1.333 ohms.

Answer 2

1 1/3 or 1.33333

Step-by-step explanation:

First of all, you should note that the answer will be smaller than the smallest resistor. That means that the answer should be less than 3. Let's see if it is.

1/R1 + 1/R2 + 1/R3 = 1/Rt

• R1 = 4
• R2 = 3
• R3 = 6

All resistors are in ohms.

1/4 + 1/3 + 1/6 = 1/Rt You could do this using decimals, but the usual way is to use fractions.

The Common Denominator is 12

3/12 + 4/12 + 2/12 = 1/Rt

9/12 = 1/Rt Turn 9/12 upside down

12/9 = Rt

1 3/9 = RT

1 1/3 = Rt

1.3333 = Rt

The answer is under 3 so we know it should be right.