Two conducting wires ‘X’ and ‘Y’ of the same diameter but made of different materials are joined in series across a battery. The number density of free electrons in ‘X’ is \( 2.5 \) times that of ‘Y’. The ratio of drift velocity of electrons in wire X to that of wire Y is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 2:5 \)
In a series connection the same current I flows through both wires, and the wires have the same cross-section A. From \( I = neAv_d \), the drift velocity is inversely proportional to the number density of free electrons.
\( \displaystyle v_d = \frac{I}{neA} \Rightarrow v_d \propto \frac{1}{n} \)
\( \displaystyle \frac{v_X}{v_Y} = \frac{n_Y}{n_X} = \frac{n_Y}{2.5\,n_Y} = \frac{1}{2.5} = \frac{2}{5} \)
So \( v_X : v_Y = 2:5 \).