Important questions on Electric current resistance and resistivity for JEE Main and Advanced

Question 1:
A cylindrical tube of length L has inner radius a and outer radius b as shown below in the figure

Given that ρ is the resistivity of the material. Find the resistance of the tube between its ends.
Question 2:
α1 and α2  are the temperature coefficient  of the two resistors R1 and R2 at any  temperature T0 0 C. Find the equivalent temperature coefficient  of their equivalent resistance  if both R1 and R2 are connected in series combination. Assume that  α1 and α2  remain same with change in temperature
Question 3:
If a copper wire is stretched to make it .2%  longer. Find the percentage change in the resistance
Question 4:
An electric current of 5 A passes through a circuit containing three wires(A,B,C) of the same material .Length of the wires in the circuit are in the ratio 2:3:4 And their diameters are in the ratio 3:4:5.Find the amount of current flowing in each branch  of the circuit  when wires are arranged in parallel combination

Question 5:
Find the equivalent resistance between point A and B in following combination of resistors

Question 6:
The current density across a cylindrical conductor of Radius A varies according to the following relation

Where K is the constant vector across the length of the conductor and x is the distance from axis.
Find the current through cylindrical cross-section

Solutions