A total resistance of 3 ohms is to be producd by combining an unknown resistor R with a 12 ohm resistor. What is the value of R and how is it connected to the 12 ohm resistor

a) 4.0 ohm parallel
b) 4.0 ohm in series
c) 2.4 ohm in parallel
d) 2.4 in series
e) 9.0 in parallel

My work: A, 1/12 + 1/4= 1/3 or 3 ohm resistance

By using only two resistors, R1 and R2, a student is able to obtain resistance of 3 ohm, 4 ohm, 12 ohm, and 16 ohm using the alone combination. The values of R1 and R2 (in ohms) are:
A) 3,4
b) 2,12
c) 3, 16
d) 4, 12
e) 4, 16

My answer is d 4,12. Since 4 is alone, 12 is alone. in series 12+4=16 and in parallel the value is 3.

thank you

correct.

12*R/(12+R) = 3

3R + 36 = 12R.
9R = 36.
R = 4 Ohms in parallel.

4, and 12 Ohms.

4 ohm Parallel is correct.

12+ 1/4 =3ohm
=> 4ohms parallel is correct

Ohm my goodness, you got it right! It looks like you've mastered the art of resistors and their combinations. Keep up the electric work!

For the first question, to find the value of the unknown resistor R, we use the formula for resistors in parallel:

1/RTotal = 1/R1 + 1/R2

Given that the total resistance is 3 ohms and R2 is 12 ohms, we substitute these values into the formula:

1/3 = 1/R1 + 1/12

Next, we solve for R1:

1/R1 = 1/3 - 1/12

Taking the LCD of 12, we simplify:

1/R1 = 4/12 - 1/12

1/R1 = 3/12

1/R1 = 1/4

Now, we take the reciprocal of both sides to find R1:

R1 = 4 ohms

So, the value of R is 4 ohms.

To determine how R is connected to the 12-ohm resistor, we need to compare the resistance values in the given options. Based on our calculation, R equals 4 ohms. Looking at the options, only option (b) states that R is connected in series with the 12-ohm resistor.

Therefore, the answer to the first question is: b) 4.0 ohm in series.

For the second question, we need to find the combination of resistors that will give us the specified resistances (3 ohm, 4 ohm, 12 ohm, and 16 ohm).

Starting with the resistance of 3 ohms, we can use the formula for resistors in parallel:

1/RTotal = 1/R1 + 1/R2

Substituting the values:

1/3 = 1/R1 + 1/R2

We can rearrange the equation to solve for R1:

1/R1 = 1/3 - 1/R2

Taking the LCD:

1/R1 = R2/3R2 - 3/3R2

1/R1 = (R2 - 3)/3R2

Now, let's analyze the given options:

a) (3,4)
b) (2,12)
c) (3,16)
d) (4,12)
e) (4,16)

Using option (a), where R1 = 3 and R2 = 4, we substitute these values into the formula:

1/R1 = (4 - 3)/(3 * 4)

1/R1 = 1/12

So, this option does not satisfy the condition of giving a total resistance of 3 ohms.

Next, we try option (b):

1/R1 = (12 - 3)/(3 * 12)

1/R1 = 9/36

1/R1 = 1/4

Therefore, option (b) is valid, as it gives a total resistance of 3 ohms.

We can repeat the same process for the other options:

c) (3,16):

1/R1 = (16 - 3)/(3 * 16)

1/R1 = 13/48

This option does not satisfy the condition.

d) (4,12):

1/R1 = (12 - 3)/(3 * 12)

1/R1 = 9/36

1/R1 = 1/4

Again, this option is valid.

e) (4,16):

1/R1 = (16 - 3)/(3 * 16)

1/R1 = 13/48

This option does not satisfy the condition.

Therefore, the valid options that give us the desired resistances are:

b) 2, 12 (gives 4-ohm resistance in series)

d) 4, 12 (gives 3-ohm resistance in parallel)

So, the answer to the second question is: d) 4, 12.

I hope this helps clarify the process and the correct answers.

D,4 ohm, series

THE ANSWER IS B, 4OHMS PARALLEL