Why are resistors useful in electric circuits?

Answer 1

The only reason i can think of this making sense is that it makes the calculation for total resistance easier. Other then that i can't see any benefit from having resistors with similar ratings.

The formula for finding total resistance in a parallel circuit is Rt=1/1/r1+1/r2+1/rn...

If all the resistors are the same, you can do the calculation in your head a lot easier.

Answer 2

The resulting resistance from 2 or more parallel resistors is the reciprocal of the sum of the individual reciprocals.

Keep in mind that the reciprocal is 1 divided by the number. So the reciprocal of 30 is 1/30 (1 divided by 30). So say we have a network of a 30 ohm resistor, another 30 ohm, a 60 ohm and a 100 ohm - 4 parallel resistors.

First we find the 4 reciprocals. 1/30 = 0.0333... Another 1/30 = 0.0333... 1/60 = 0.01666... 1/100 = 0.0100

Now we add the 4 reciprocals: 0.0333 + 0.0333 + 0.01666 + 0.0100 = 0.09333

Finally, take the reciprocal of the above sum: 1/.09333 = 10.71 ohms.

The number of significant digits to carry depends on the tolerance of the resistors and the final tolerance required. The effect each tolerance will have on the total is the tolerance of each resistor times the total resistance divided by that resistor's value. So in the above problem, each 30 ohm resistor's effect on tolerance will be their own tolerance times 10.71/30.

Answer 3

It may or may not be so. If one resistor of the arrangement completely fails, then in a series circuit the resistance becomes infinite. In a parallel circuit the resistance will rise to the value determined by the remaining resistors. Which of those results is better or worse depends on the application.

Answer 4

We connect resistances in parallel in order to reduce the output resistance.

Answer 5

limit current flow