What is the difference in the energy consumed by three resistors of 10 ohm, 25 ohm, 20 ohm if they are attached in series and in...

We know that when two resistors a and b are connected in
series the equivalent resistance of the system is a + b. Now we are given the three
resistors as 10 ohm, 25 ohm and 20 ohm. When they are connected in series the equivalent
resistance is 10 + 20 + 25 = 55 ohm. When the combination is connected across a voltage
V the energy consumed is V^2/ R = V^2/ 55.

Now, when two
resistors a and b are connected in parallel the equivalent resistance is given as (1/a +
1/b) ^ (-1). So for the three resistors connected in parallel the equivalent resistance
is (1/10 + 1/20 + 1/25) ^-1 = (0.1 + 0.05 + 0.04) ^-1 = 1/ 0.19 = 5.26 ohm. Now the
energy consumed is V^2 / 5.26

So we can see
that the resistors in parallel consume more energy than they do when they are connected
in series.