The resistance of 2 resistors R1&R2 is a parallel circuit is given by the formula:?

Question

RI=(1) over 1/r1+1/r2 I do not get it at all? Help

Answer 1

For parallel circuit, the voltage is a contant. Therefore,
v = I1r1 = I2*r2 = (I1+I2)r
I1 = v/r1, the current through r1
I2 = v/r2, the current through r2

r, the total resistance
= v/(I1+I2)
= v(v/r1 + v/r2)
= 1/(1/r1 + 1/r2)
= r1*r2/(r1+r2)

Answer 2

it helps to think of the current flow. current = voltage / resistance.
imagine if there was only one resistor, the current would be so much.
if you put another resistor in parralel, then there is another path for the current to flow. so more current flows. so the total resistance has to be lower than for just one resistor.
so the total resistance Rt has to be a lower number than either of R1 or R2.
again look at it from the point of view of the current.
current for R1 would be voltage / R1
current for R2 would be voltage / R2
the total current would be voltage / R1 + voltage / R2. see how that is similar to the equation for Rt?
so finally if you generalize the equations, 1/ R is the same as 1/R1 + 1/R2
or 1/Rt = 1/R1+ 1/R2
then you do an algabreic move to put Rt on top and
Rt = 1 / (1/R1 + 1/R2)
hope the explanation helps

Answer 3

Lets call the resistance of the parallel circuit Rt and the individual resistance R1 and R2, then

1/Rt = 1/R1 + 1/R2

If you rearrange the equation, you have

Rt = 1 / (1/R1 + 1/R2)

Intuitively, you could view the resistance as the opposite of conductivity, lets call conductivity Ct = 1/Rt, and C1 = 1/R1 and C2 = 1/R2. Intuitively, you can see this makes sense as an infinite resistance would have zero conductivity, while zero resistance will allow infinite conductivity.

Then Ct = C1 + C2
and you can substitute the C's with the 1/R's.

Does this help?

Answer 4

just remember in parallel cicuits with resistors:
R total= the product divided by the sum=(R1*R2)/(R1+R2)

Answer 5

Rt = 1/(1/R1 +1/R2) --> 1/Rt = 1/R1 +1/R2 =(R1+R2)/(R1*R2) So Rt = R1*R2/(R1+R2)

Answer 6

Please clarify your question... Do you not understand the formula? Or do you not understand how a parallel circuit works? Is this for a circuits class or physics electromagnetics class?