Question

A potentiometer wire of length 100 cm has a resistance of 10 `Omega.` It is connected in series with a resistance and an accumulator of e.m.f 2 V and of negligible internal resistance. A source of e.m.f 10 mV is balanced against a 40 cm length of the potentiometer wire. The value of the external resistance is ____________.

Options

• `395  Omega`

• `790  Omega`

• `405  Omega`

• `810  Omega`

Answer 1

A potentiometer wire of length 100 cm has a resistance of 10 `Omega.` It is connected in series with a resistance and an accumulator of e.m.f 2 V and of negligible internal resistance. A source of e.m.f 10 mV is balanced against a 40 cm length of the potentiometer wire. The value of the external resistance is `790  Omega`.

Explanation:

`"I" = 2/ "R" + 10`

`therefore "V" = "I R"_"AB" = 2/("R" + 10) xx 10`

` = 20/"R" + 10`

`therefore "V"/"L" = 20/(("R" + 10) xx 1) = 20/("R" + 10)`

`"E"_1 = l ("V"/"L")`

`therefore 10 xx 10^-3 = 0.4 (20/("R" + 10))`

`therefore "R" + 10 = 8/10^-2 = 800`

`therefore "R" = 790  Omega`