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Write the principle of working of a pote...

Write the principle of working of a potentiometer. Describe briefly, with the help of circuit diagram, how a potentiometer is used to determine the internal resistance of a given cell.

Text Solution

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Working principle: When constant current flows through a wire of uniform cross section then potential difference across the wire is directly proporational to the length.
`V alpha l`

With key `K _(2)` balance is obtained at length `l _(1) (AN _(1)).` Then,
`epsi = phi l _(1)` (`phi=` potential gradient)
When key `K _(2)` is closed, the cell sends a current (I) through the resistance box (RB). If V is the terminal potential difference of the cell the balance is obtained at length `l _(2) (AN _(2)).`
`V = phi l _(2)`
implies `(epsi )/(V) = (l _(1))/( l _(2))`
But `(epsi )/( V) = (I ( R+r ))/( IR) = (1 + (r )/( R ))`
` therefore (1 + (r )/( R)) = (l _(1))/( l _(2))`
`implies r = (( l _(1) - l _(2)))/( l _(2)) R`
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Knowledge Check

  • The length of a wire of potentiometer is 100 cm, and the e.m.f. of its standard cell is E volt. It is employed to measure the e.m.f. of a battery whose internal resistance is 0.5 Omega . If the balance point is obtained at l = 30 cm from the positive end, the e.m.f. of the battery is:

    A
    `(30E)/(100.5)`
    B
    `(30E)/(100-0.5)`
    C
    `(30(E-0.5i))/100`, where i is the current in the potentiometer wire
    D
    `(30E)/100`

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