Two lamps can be connected to a battery in a circuit in series or in parallel. You can calculate the total resistance RT (t is down from r) in a circuit if you know the resistance in each lamp. Resistance is measured in ohms. For a circuit connected in series, RT = R1 + R2. For a circuit connected in parallel, 1/RT = 1/R1 + 1/R2.

a. The lamps are connected in parallel. RT = 12 ohms. Find R2.

just plug it into the formula:

1/12 = 1/R1 + 1/R2
Unless you know R1, you can't figure R2. If the lamps are identical, then R1=R2=24

I'm sorry, R1 = 30 ohms.

How do I do 1/12 = 1/30 + 1/R?

1/R = 1/12 - 1/30

1/R = 1/20
R = 20

To find the value of R2 in a parallel circuit given that the total resistance RT is 12 ohms, we can use the formula for calculating the total resistance in a parallel circuit:

1/RT = 1/R1 + 1/R2

Since RT is given as 12 ohms, we can substitute it into the formula:

1/12 = 1/R1 + 1/R2

To solve for R2, we need to rearrange the equation. First, we can subtract 1/R1 from both sides of the equation:

1/R2 = 1/12 - 1/R1

Next, we can take the reciprocal of both sides to isolate R2:

R2 = 1 / (1/12 - 1/R1)

This equation gives us the value of R2 in terms of the given resistance R1 and the total resistance RT.