Hello, I am not sure how to go about solving this equation:
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. Find the resistance of the second resistor if the total resistance of the pair is 1.7 ohms.
I'm not sure how to go about this I thought maybe:
1/1.7=1/2.3+1/x
I've never done anything like this before
Ok so far
Don't let the fractions scare you
1/1.7 - 1/2.3 = 1/x
.15345 = 1/x , take reciprocal of both sides, (flip it)
1/.15345 = x/1
x = 6.5
check: 1/2.3 + 1/6.5 = .5886
1/1.7 = .2882 (close enough)
Ok, thanks. That's actually what I have in my notebook. I just wasn't sure if I was going about it right.
To solve the given equation, you are on the right track. Let's go step by step:
1. Start with the equation you wrote: 1/1.7 = 1/2.3 + 1/x.
2. The equation represents the relationship between the total resistance (1/1.7) and the resistances of the two parallel resistors (1/2.3 and 1/x).
3. To simplify the equation, we need to find a common denominator. The least common denominator between 1/2.3 and 1/x is 2.3x. Multiply each term by 2.3x to get rid of the fractions:
2.3x * (1/1.7) = 2.3x * (1/2.3) + 2.3x * (1/x).
4. Simplify the equation:
1.35x = x + 2.3 * 1.7.
5. Further simplify:
1.35x = x + 3.91.
6. Rearrange the equation to isolate x:
1.35x - x = 3.91.
0.35x = 3.91.
7. Divide both sides of the equation by 0.35 to solve for x:
x = 3.91 / 0.35.
8. Calculate the value of x:
x ≈ 11.2 ohms.
Therefore, the resistance of the second resistor is approximately 11.2 ohms.