Resistors is series add normally, resistors in parallel are the inverse sum of the inverses. When you have two 100Ohm resistors in the loop containing R5 and R6, the equivalent resistance of that loop is 200Ohms. That leg now has twice the resistance as the R3 leg and therefore gets half of the current. The question is asking if the equivalent resistance will change if you bridge R3 with wire, removing the load. The result is that you've shorted your circuit and now zero current passes through R5 and R6 because the current finds zero resistance across the straight wire.

It's really a simple question from the PDF:

"Would the equivalent resistance of the circuit increase, decrease or stay the same if R3

was replaced with a wire?"

If you replace R3 with a wire you are shorting that junction and eliminating all 3 resistors, leaving only R1 and R2. So your total circuit resistance decreases from 266 Ohms to 200 Ohms. This means current flowing through the circuit will increase.

There is the same *voltage* across R3 and the series combination of R5 and R6.

R3 is 100 ohms. R5 and R6 add to 200 ohms, As there's the same voltage across R3 and (R5 and R6 together), there is more current in R3 because it has the lower resistance.

The total resistance as seen from the battery is 266.667 ohms. The current is 33.75mA. The V-drops across R1 and R2 are 3.375V each so the voltage across R3 and R5,6 is 2,25V. The current splits.

You can use ohms law to find the current or you can use the opposit over the sum.

33.75mA ( R5,6 / R3+R5,6)= 33.75*200/300= 33.75* 2/3 =22.5 mA the other branch is 33.75-22.5=11.25mA.

The current splits by the ratio of the resistances. The higher current going to the lower resistance.

The current always splits as an R1 / R1+R2 ratio. or I*R1+R3 / R1+R2+R3 for the current in R2.

You will have to play with this to see it. It takes practice. learn to do it in Excel. Excel keeps things straight for you and allows you to chain results.

In a parallel circuit the voltage measured across all loads (resistance) is the same...therefore each different resistor will have different amounts of electron flow per second.