A potentiometer wire of length 100 cm has a resistance of `10 Omega`. It is connected in series with a resistance `R` and cell of emf `2 V` and negligible resistance. A source of emf 10 mV is balanced against a length of `40 cm` of the potentiometer wire. What is the value of `R`?

Explanation

From the theory of potentiometer `V_(cb)=E` if no current is drawn from the battery
or `(E_1/(R+R_(ab)))R_(cb)=E`
Here, `E_1=2V, R_(ab)=10Omega, R_(cb)=(40/100)xx10=4Omega` and `E=10xx10^-3V`

Substituting in above equation we get
`R=790Omega`