Physics question?

Question

Several resistors with equal resistances of 100 Ohms are connected in a parallel circuit. The total resistance of that circuit is 20 Ohms. How many resistors are connected in the circuit?

Most detailed answer will get 10 points.

Thanks for the help.

Answer 1

to find the sum of the resistance in parallel circuit, add the reciprocal of each resistors, than take an inverse

Sum = (1 / R1 + 1 / R2 + ..... + 1/Rn)^-1

Because we don't know how many resistors there are, we can't use the equation above. However, there is a concept about adding the resistors that are equal magnitude of resistance.

say you add 2 100-ohm resistors, the total will be 50 ohm

say you add 3 100-ohm resistors, the total will be 33 1/3 ohm

say you add 4 100-ohm resistors, the total will be 25 ohms

Do you see the pattern, the sum is equal to 1/n of the resistors.

n = number of resistors.

when there are 2 resistors that have equal magnitude in resistance, the total will be 1/2 of that resistance.

when there are 3 resistors that have equal magnitude in resistance, the total will be 1/3 of that resistance.

when there are 4 resistors that have equal magnitude in resistance, the total will be 1/4 of that resistance.

20 / 100 = 1/5

the sum is equal 1/5 of 100, thus, there are 5 resistors that have 100-ohms

Hope this helps

Answer 2

Hi, when n resistors with the the same resistance R are parallel to each other and the voltage over each resistor is the same than the reciproke value of the total resistance 1/Rtot equals the sum of all reciprokes 1/R.


1/Rtot = n*1/R > n = R/Rtot = 100/20 = 5

This follows from Ohm`s law applied to n parallel resistors. Through each resistor flows a current I equal

J = U/R

Given are n parallel resistors R. Therefore we get the total current Jtot
Jtot = n*J = n*U/R

Ohm`s law also says

Jtot = U/Rtot

From here we get 1/Rtot = n*1/R and

n = R/Rtot

Answer 3

Well, for parallel resistors, we know that the equation is:

1/Req = 1/R1 + 1/R2 + ...

So, we want 1/20 = 1/100 + 1/100 + ....., but we don't know how many terms we need. Well, since each 1/100 term is equal, we could make it a summation:

1/20 = n*(1/100), where n is the number of resistors. Now, we could put it in decimal form, which will make it easier to see the answer:

.05 = n*.01

We can divide by .01 on both sides to solve, and you quickly see that n=5.

Thus, there are 5 parallel resistors in this circuit.

Answer 4

There are 5-100 ohm resistors in parallel.

For resistances in parallel the network resistance is the reciprocal of [the sum of the reciprocals of each resistance].

The bracketed quantity above is N (1/100), where N is defined to be how many 100 ohm resistors you have in parallel in the network (and you have stated each resistance is 100 ohms).

So the bracketed quantity is N/100, and its reciprocal is 100/N which you've stated is 20 ohms for the network.

Solving for N gives 5.

Answer 5

Rt = 1/((1/R1) + (1/R2) + ....) which, for equal valued resistors, becomes
Rt = R/n where n is the number of resistors. With 100Ω resistors, 5 in parallel will equal 20Ω

Doug

Answer 6

30 resistors.

600 ohms
----- = 20 ohms
30 resistors

Answer 7

right on doug!

5- dont know how i know that...

Answer 8

4.5