What is the theory behind voltage dividers and current dividers?

[logearav]

friends,
what is the role of potential or voltage divider in a circuit? in an operational amplifier circuit, while applying inputs to non inverting input, when two resistances are connected are connected across the battery they said to form a voltage divider. if the first resistance is r3 and second one is r4 which is grounded, the equivalent equation is r4/(r3+r4). what is the theory involved in voltage divider and current divider? also what is the theory behind this equation. help in this regard will be greatly appreciated. please refer my attachment provided

 

[willem2]

By choosing an appropriate R3 and R4 you can make the +input of the op-amp any desired fraction of V2.
It works because the current through R3 and R4 is the same, so the voltages across them will be I*R3 and I*R4. The current is equal to V2/(R3+R4), so the voltages across R3 and R4
will be
V2*R3/(R3+R4) and V2*R4/(R3+R4)

 

[arithmetix]

Hi Logearav
There is a wonderful text which very simply explains the things you seem to want to know:
Authors: Horowitz and Hill
Title: The Art of Electronics.

 

[logearav]

thanks a lot members