Two cylindrical wires, A and B, are made of the same conducting material. The radius of wire A is twice the radius of wire B. If wire A carries a current that is three times the current carried by wire B, what is the ratio of the drift speed of electrons in wire A to that in wire B?

Step-by-step solution

The drift speed of electrons in a conductor is given by v_d = I neA Since both wires are made of the same material, the free electron density n is the same for both wires. The cross-sectional area is A = r^2 . Therefore, the drift speed is proportional to I r^2 Given that r_A = 2r_B and I_A = 3I_B The ratio of drift speeds is v_ dA v_ dB = ( I_A I_B ) ( r_B r_A )^2 Substituting the given values: v_ dA v_ dB = (3) ( 1 2 )^2 = 3 4 The ratio of the drift speed of electrons in wire A to that in wire B is 3 : 4 . Answer