Two wires X, Y have the same resistivity, but their cross-sectional areas are in the ratio 2:3 and lengths in the ratio 1:2. They are first connected in series and then in parallel to a d.c. source. Find out the ratio of the drift speeds of the electrons in the two wires for the two cases.

Explanation

Here, it is given that `rho_X = rho_Y ` but ` (A_X)/(A_Y) = 2/3 ` and `(l_X)/(l_Y) = 1/2`
` therefore (R_X)/(R_Y) = (rho_X)/(rho_Y) xx (l_X)/(l_Y) xx (A_Y)/(A_X) = 1 xx 1/2 xx 3/2 = 3/4`
We know that current `I = nAe v_d` or drift speed `v_d = (I)/(nAe)`
(i) When wires X and Y are joined in series to a d.c. source, current I flowing through them is same. Moreover, for same material free electron density n is also same. Hence,
` therefore ( (v_d)_X)/((v_d)_Y) = (A_Y)/(A_X) = 3/2`
(ii) When wires X and Y are joined in parallel to a d.c. source, voltage across both wires is same. Hence
`v_d = (V)/(RnAe) `
`((v_d)_X)/((v_d)_Y) = (R_Y)/(R_X) . (A_Y)/(A_X) = 4/3 xx 3/2 = 2/1`