The formula for the total resistance RT (in ohms) of a parallel circuit is given by

rt= 1 / ((1/r1)+(1/r2)+(1/r3))
where R1, R2, and R3 are the resistance values of the first, second, and third resistors, respectively.
Simplify the total resistance formula.

hello, why no response

10

Sure, I'd be happy to help you simplify the total resistance formula for a parallel circuit. But before we start, remember that as a clown bot, I'm here to bring a smile to your face, not to bore you with complicated formulas. So let's make it a little more interesting, shall we?

Imagine you have a group of clowns trying to squeeze into a tiny clown car, each clown representing a resistor. The more clowns you have, the easier it is to squeeze in, because the resistance decreases. Now, let's get started with the simplification!

To simplify the formula, we can start by getting rid of those pesky fractions. We do this by finding a common denominator for all the resistors. In this case, the common denominator is R1 * R2 * R3.

So, the simplified formula for total resistance in a parallel circuit is:

RT = (R1 * R2 * R3) / (R2 * R3 + R1 * R3 + R1 * R2)

It may look a bit jumbled, but trust me, it's simpler than the original formula. And hey, at least I didn't ask the clowns to perform any acrobatics while squeezing into the car!

To simplify the total resistance formula for a parallel circuit, we can start by finding a common denominator.

Recall that the formula for adding fractions requires a common denominator. In this case, the common denominator will be r1 * r2 * r3.

Next, we can rewrite the formula using the common denominator:

rt = 1 / ((1/r1)+(1/r2)+(1/r3))

Multiplying each term in the denominator by the respective resistances, we get:

rt = 1 / ((r2 * r3 / (r1 * r2 * r3)) + (r1 * r3 / (r1 * r2 * r3)) + (r1 * r2 / (r1 * r2 * r3)))

Combining the fractions, we get:

rt = 1 / ((r2 * r3 + r1 * r3 + r1 * r2) / (r1 * r2 * r3))

Simplifying further, we can cancel out r1, r2, and r3 in the numerator and denominator:

rt = 1 / ((r2 * r3 + r1 * r3 + r1 * r2) / (r1 * r2 * r3))
= (r1 * r2 * r3) / (r2 * r3 + r1 * r3 + r1 * r2)

Therefore, the simplified formula for the total resistance of a parallel circuit is:

rt = (r1 * r2 * r3) / (r2 * r3 + r1 * r3 + r1 * r2)

c'mon. This is just algebra I

You have
1/R = 1/R1 + 1/R2 + 1/R3
The LCD is R1*R2*R3, so
1/R = (R2*R3 + R1*R3 + R1*R2)/(R1 R2 R3)
now just flip both sides.
R = (R1 R2 R3)/(R2*R3 + R1*R3 + R1*R2)