Question

In a discharge tube the number of hydrogen ions drifting across a cross section per second is n₁ while the number of electrons drifting in the opposite direction across another cross section is n₂ . If the supply voltage is V, the effective resistance, of the tube is

(1) \(\frac{V}{(n_1 -n_2)e}\)

(2) \(\frac{V}{(n_1 +n_2)e}\)

(3) \(\frac{eV}{n_1 -n_2}\)

(4) \(\frac{eV}{n_1+n_2}\)

Answer 1

 (2) \(\frac{V}{(n_1 +n_2)e}\)

The effective current in the tube will be obtained by adding the current due to flow of protons in one direction and the flow of electrons in opposite direction. Hence the total current through the tube is (n₁ +n_e)|e|. 

Now from Ohm’s law, the resistance of the tube is given by