Question

When resistors are connected in parallel, we can be certain that:

a) their equivalent resistance is greater than the resistance of any one of the individual resistances.

b)the potential difference across each is the same.
c)the same current flows in each one.
d)the power dissipated in each is the same.

Answer 1

b)the potential difference across each is the same.

Answer 2

b)the potential difference across each is the same.

Answer 3

b)the potential difference across each is the same.

Answer 4

Two resistors in parallel have less overall resistance than the same two resistors in series, or even just one of the resistors by itself. This is becausetwo resistors in parallel draw more current than just one resistor -- assuming constant voltage. If the voltage remains constant and the current increases,then Ohm's Law (V=IR) dictates that the resistance must decrease.

When you have resistors in parallel, you can compute the total resistance fairly easily with simple math. The special case of having two resistors inparallel is interesting and easy to remember. To compute the total (or apparent) resistance of two resistors in parallel, just divide the product of theresistance values by their sum. Let's say you've got a 3-ohm resistor in parallel with a 6-ohm resistor. The total resistance is 6*3/(6+3) = 18/9 = 2. So,the total resistance of those two resistors in parallel is two ohms. If you've got two identical resistors in parallel, the resistance is exactly half thevalue of one resistor. Two 10-ohm resistors in parallel have a resistance of five ohms. Two 100-ohms resistors have a resistance of 50. Two 150Kohmresistors have a value of 75Kohm.

If you've got a bunch of resistors in parallel, here's what you do. Add up all the reciprocals of the resistance values. Then find the reciprocal of thatsum. Your answer should be less than the lowest-valued resistor in your R-ladder. If it's not, you hosed the calculation.

Try the following: Calculate the resistance of the following resistors in parallel (assume ohms for each): 2, 4, 8, and 16. You should come out with 16/15ohms, which equals 1.067 ohms.

I know some of you want to see the math.

First, add up the reciprocals: 1/2 + 1/4 + 1/8 + 1/16 = 8/16 + 4/16 + 2/16 + 1/16 = 15/16.

Next, take the reciprocal of that answer: 16/15 = 1 and 1/15 = 1.067 ohms.