Two wires A and B of same material having length L_A, L_B and radii R_A, R_B and drift velocity v_A, v_B respectively carries same current. If L_A=L_B and R_A=2 R_B then the value of ( v_A v_B ) is

Step-by-step solution

Current through a wire is given by I=n e v_d A=n e v_d R^2 Here, n = number density of free charge carriers v_d= drift speed of electrons R= radius of wire e= charge on an electron Here, for two wires A and B aligned & I_A=I_B (given) & n_A=n_B (wires have same material) aligned R_A=2 R_B (given) so we have, I_A=I_B n e v_A R_A^2=n e v_B R_B^2 array ll & v_A v_B = ( R_B R_A )^2= ( R_B 2 R_B )^2 & v_A v_B = 1 4 =0.25 array