Find the value of x if P is a null point

Explanation

Current in the main circuit
200 -25 I -75i=0
i=2A
Potential gradient `=(150V)/(10m)=15V//m`

For 120 V
`rArr(120V//m)/(15V)=8m`
`thereforex=10-8=2m`
Now we will analyse the other task to find internal resistance of the cell using potentiometer . The main key point is that first analyse the main circuit then the axuillary circuit (supplementary circuit)
Potential gradient `=(E_(1))/(l)`
Now for the auxillary circuit

`i=(E)/(R+r)`
`E-ir=E-(Er)/(R+r)=(ER)/(R+r)`
`therefore(ER)/(R+r)=(E_(1))/(l)x`
Let we take some examples to understand the topic in better way.