Electric Current

Problems from IIT JEE

Problem (IIT JEE 1997): A steady current flows in a metallic conductor of non-uniform cross-section. The quantity/quantities constant along the length of the conductor is (are),

  1. current, electric field and drift speed
  2. drift speed only
  3. current and drift speed
  4. current only

Solution: In steady state, charge can not accumulate in a conductor. Thus, constant current $i={\mathrm{d}q}/{\mathrm{d}t}$ flows along the length of conductor. The current density at a point having cross-section area $A$ is given by $J={i}/{A}$. The current density is related to electric field by $J=\sigma E$, where conductivity $\sigma$ is a material property. The drift velocity $v_d$ is given by $i=neAv_d$. Thus, both $E$ and $v_d$ are inversely proportional to $A$.