... connected in series and then parallel in a circuit across the same potential difference. calculate the ratio of heat produced series and parallel combination
Answers (1)
These are basic principles, so what you need to do is review the chapter and learn the material. You need to understand the section perfectly before you go on. Here is a free course in the basics: www.phy.davidson.edu/instrumentation/NEETS.htm
All the words about the wires only say they have the same resistance, so you have w=I^2R for each case. In the series case I = E/(2R) and in the parallel case I = 2E/R.
Series w = (E/(2R))^2 x R = E^2/(4R)
Parallel w = (2E/R)^2 x R = 4E^2/R
Ratio is one number over another, and you have not specified which, but it is easy enough to figure out.
ratio = (E^2/(4R))/4E^2/R) = (R/(4E^2)) x E^2/(4R) = 1/16 << ANSWER
It would also be correct to turn the ratio over and say that one is 16 times the other. That is a ratio of powers. "Heat" is a little more complicated, being a function of time. It is a very common mistake to think that heat, temperature, and power are all the same.