Question

When a pair of identical resistors are connected in series, which of the following is the same for
both resistors :
(a) voltage across each (b) current through each.
Do any of your answer changes if resistors are different from each other ?​

Answer 1

Answer:

The most straightforward way to reason about this doesn't require much math.

The power delivered by the voltage source to either pair of resistors is inversely proportion to their combined resistance, i.e, if the combined resistance is greater, the power delivered is smaller.

pR=V2R

Now, recall that:

the series combination of two resistances is always greater than either individual resistance

the parallel combination of two resistances is always less than than resistance of either individual resistance

For example, suppose that both resistors have the same value of resistance R.

Now, if the two resistors are connected in series, the equivalent resistance is REQ=2R.

But, if the two resistors are connected in parallel, the equivalent resistance is REQ=R2.

Thus, the power for the series combination is:

pseries=12V2R

Whilst the power for the parallel combination is:

pparallel=2V2R

In this case, the parallel combination dissipates 4 times the power of the series combination.