Yes two resistors of R1 and R2 whatever that means…so basically i am trying to simplify the formula, but this is not going to be easy, if i don’t understand the theory from the beginning………
The simplest formula for the effective resistance of 2 resistors in parallel is:
1/Rt = 1/R(1) + 1/R(2)
where Rt is the effective resistance and R(1) and R(2) are the resistance of the two resistors in paralel. You see when you place two resistors in parallel, the effective resistance of the two is always lower than either one resistor by itself. You can think about it this way: the resistor is like a narrow door which the electricity must pass through, so the higher the resistance is, the narrower the opening. When you just have one resistor, it is like only allowing the electricity to pass through one door. However, when you have two resistors in parallel, you oƿє-ṅєd a second door right besides the frist one for the electricity to pass through. Therefore the overall flow of electricity is increased and the effective resistance of the two resistors in parallel is lower.
When you put two resistors in series, on the other hand, is like putting a narrow door behind another narrow door, so it’s harder for the electricity to get through both doors and the effective resistance goes up.
R(s) = R(1) + R(2)
The general formula is
1/Rt = 1/R1 + 1/R2 + 1/R3 + …
What this means physically is that in resistors in parallel, the conductances add. (I.e., for a given applied voltage, the currents add.) Conductance of a resistor R is 1/R. If you want to see only Rt on the left side,
Rt = 1/(1/R1 + 1/R2 + 1/R3 + …)
For two resistors only, the general formula can be algebraically morphed to
Rt = R1 * R2/(R1 + R2).
Note that the dimension of the right side of this formula is R^2/R, or simply R. You can’t extend this formula to more than two resistors because then the dimension would be at least R^3/R or R^2.
If you meant Rt = 1/R1 + 1/R2 then you combine both fractions into one as follows:
Rt = R2/R1R2 + R1/R1R2 = (R2+R1)/R1R2
If you meant Rt= (1)/1/R1 + 1/R2 then
Rt= R1 + 1/R2 = R1R2/R2 + 1/R2 = (R1R2+1)/R2
If that’s not what you meant then you’ll have to edit your question and give more details.
simplfy for what?? looks like you are trying to find the effective resistance of two parallel resistors.