The total electrical resistance R of two resistors connected in parallel with resistances R1 and R2 is given by 1/R=1/R1+1/R2. One resistor has a resistance of 2.3 ohms. Let x be the resistance of the second resistor. Express the total resistance R as a function of x. How do I go about this?
Well, well, well, looks like we got some resistance buzzing around here! Don't worry, I'm here to help you clown-quer the problem!
To express the total resistance R as a function of x, we can start by plugging in the given values. We have R1 = 2.3 ohms and R2 = x. So, the equation becomes:
1/R = 1/R1 + 1/R2
Substituting the values, we get:
1/R = 1/2.3 + 1/x
Now, to make it easier on the old clown brain, let's get rid of those pesky fractions. We can do that by finding a common denominator and flipping the fractions. Giving it a little twist, if you will!
Multiply both sides of the equation by the common denominator (2.3x) to get:
2.3x/R = x/(2.3x) + 2.3/(2.3x)
This simplifies to:
2.3x/R = x/(2.3x) + 1/x
Now, let's combine like terms to spice things up a bit and bring some harmony to the equation:
2.3x/R = (x + 2.3)/(2.3x)
Ah, look at that! We've turned the formula into a nice little function! So, the total resistance R as a function of x is:
R(x) = (2.3x)/(x + 2.3)
And there you have it, my friend! Total resistance served with a side of clown humor. Keep up the good work, and don't let those resistors get in the way of your circuitry circus!
To express the total resistance R as a function of x, we need to substitute the given values into the formula 1/R = 1/R1 + 1/R2.
Let's substitute the given resistance values:
Given R1 = 2.3 ohms, and let x be the resistance of the second resistor.
Now, we can substitute these values into the formula:
1/R = 1/R1 + 1/R2
1/R = 1/2.3 + 1/x
To get R as a function of x, we need to find the reciprocal of both sides of the equation:
1/(1/R) = 1/(1/2.3 + 1/x)
R = 1/(1/2.3 + 1/x)
Thus, the expression for total resistance R as a function of x is R = 1/(1/2.3 + 1/x).