Question

When two resistors are wired in series with a 12 V battery, the current through the battery is 0.30 A. When they are wired in parallel with the same battery, the current is 1.6 A. What are the values of the two resistors?

Note: I understand other people have asked the same concept with different numbers, and their questions have been answered, however I do not understand why you need to multiple R1 by R2 when the resistors are in parallel, and furthermore, why are you supposed to multiply the "in parallel" equation by (R1+R2; the in series resistors) to find R1*R2? If someone can please solve this problem, while explaining also why those steps are done, it would be greatly appreciated! Thanks!

Answer 1

When two resistors and are connected in series, the same amount of current passes through them.

Effective resistance of the combination is

The current through the battery with voltage is , then   ( Ohm's law)

-------------

When two resistors and are connected in parallel, the voltage across the two resistors is same.

That is

Effective resistance of the combination is

Voltage across the battery is

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For the given problem:

, current through the battery for series combination is

--------(1)

Current through the battery for the parallel combination is

---(1)

Adding (1) and (2)

from (2)