A circuit has four resistors (all with different resistances) and a single ideal

Question

A circuit has four resistors (all with different resistances) and a single ideal battery. The circuit has both parallel and series connections (the resistors aren't all in series, or all in parallel).

If a fifth resistor is added to the circuit, connected in parallel with one of the original four resistors that doesn't initially have a parallel connection, will the original resistors end up with higher or lower currents than before?

The fifth resistor has a different resistance from the other four. All five resistances should be of the same order of magnitude (the largest resistance should be no more than 4-5 times as big as smallest resistance in the experiment).

Your solution should show complete diagrams for both the "before" and "after" circuits. Use additional diagrams to help illustrate the process of finding the currents for each of the resistors.

I know that the resistor will end up with lower currents than before but I don't know how to show that with equations.

Explanation / Answer

In parallel circuit

1/Req = 1/R1 + 1/R2

=> net resistance Req is lower than individual resistances R1 and R2 .

As, Inet = V/Req

=>   If a fifth resistor is added to the circuit, connected in parallel with one of the original four resistors that doesn't initially have a parallel connection , the original resistors will end up with higher currents than before .

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