Some new things I discovered about potentiometer when mugging dc circuit last night.

Firstly, the derivation of a formula to calculate internal resistance of a battery without using stupid formulae such as v=ri and v=e-ir. (Refer to diagram on page 10 of dc notes)


Advantage: can do a lot of simple questions with this formula, such as example 6 in notes.
Disadvantage: realise a lot of cheem-er questions such the one in tutorial wickedly alter their first circuit. as such you cannot use this formula.

Secondly, the realisation that the value of current is the same for both circuits in the potentiometer.

I know this one sounds a bit weird because there is supposed to be no current flowing through the second circuit. But I proved it both common sensically and mathematically.

Common sense proof:
Since both circuits kinda share a portion of the long resistance wire, and the potential difference between the portion of wire and its resistance are always constant, it follows that the current for that portion of wire is the same for both circuits. Since current is same throughout a circuit, the currents for both circuits are the same.

Mathematical proof:

(In the middle part, I separated the circuit just to make sure stubborn ppl who refuse to admit that there is current can see the current.)

Advantage: can do no matter how cheem questions (such as the challenging question in tutorial) very fast, as long as there are only two circuits. simply use V1/R1=V2/R2.
Disadvantage: cannot do questions which got extra resistors connected parallel to the second circuit. (like the set-up which is used to determine internal resistance)