When 2 resistors are connected in parallel the effective resistance is observed as 8.5 Ohms. Find the individual resistances if R2 is half of R1's resistance.
Answers
Answer:
here
Explanation:
While knowing the formulas for solving this is a must, I solved it in my head in a couple of seconds using this logic.
The two values must add up to nine.
In parallel, the highest value possible is two equal resistors adding up to 9 which would be 4.5. Two equal value resistors in parallel have a total value of 1/2 or 2.25.
In parallel, the total resistance is always less than the lowest value resistance. Since the parallel resistance =2, the lower resistor must be more than 2.
Assumption - The answer consists of two whole numbers because this is a quiz.
This leaves me with two possible answers if my assumption is correct, either 4 and 5 or 6 and 3.
At this point, having the ability to visualize graphs in your head is necessary. I can see the slope of the graph with two known points of A (4.5 and 4.5) = 2.25 and B (2 and 7) = less than 2. When I mentally plot 6,3 and 5,4 by dividing the line between the know points into three segments, it is obvious that 6,3 is the closer value to 2.
Then I checked my answer which was correct.
After trying to explain this, I can see this "talent" is a lot harder to explain to someone than it is for me to do. What advantage do I have from doing this in my head? Well I worked in a calibration lab for years where I would have to dig out two resistors from bins that came within 1% of a calculated value (or measure value from a decade box) to solder into a circuit to make a meter read properly. You seldom found the exact value resistor and needed to get close with what you had quickly.
I’m not giving the formula because this is a homework question. You need to ponder over how series and parallel resistors work and know this so well, it is easy.
Answer:
even though the day was a table