Two identical wires X and Y, each of length L carry the same current I. Wire X is bent to form a square of side a and wire Y is bent into a circle of radius R. If \( B_x \) and \( B_y \) are the values of the magnetic field at the centres of the square and the circle respectively, the ratio \( B_x : B_y \) is

Four materials \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) and D have the magnetic susceptibilities \(\chi_{m A}, \chi_{m B}, \chi_{m C}\) and \(\chi_{m D}\) respectively. which are related as \(\chi_{m D}<\chi_{m C}<\chi_{m B}<\chi_{m A}\). Which material can be magnetised with maximum ease?

When monochromatic orange light is used instead of violet light in a convex lens, its focal length will :

The transfer of integral number of ____________ is one of the evidence of quantization of electric charge.

A current of \(1.0\) mA is flowing through a potentiometer wire of length 4 m and of resistance \( 40 \, \Omega \). The potential gradient of the potentiometer wire will be :

eV (electron volt) is the unit of

In a coil, the current is changed from 12 A to 24 A in 1 s. The self-induced emf of the coil is 24 V. The change in energy in the coil is

Which one of the following is NOT a method of molecular diagnosis for early detection of a disease?

Vector in the direction of \(\hat{i}+\hat{j}+\hat{k}\) with magnitude 5 units is :

Let \(A, B, C\) be matrices of order \(p \times k, 3 \times k\) and \(n \times 3\) respectively, then the conditions on \(n, k\) and \(p\) so that \(A B+C B\) will be defined are :

Relation \(R\) on the set \(A=\{1,2,\)...,\(15\}\) defined as \(R=\{(x, y): y-4 x=0\}\) is

Which of the following is not an alien species in India?

Read the passage carefully and answer the questions
The resistance ( \(R\) ) of an object is given by the expression \(R=\rho \frac{l}{A} .\)
The inverse of \(R\) is called conductance and the inverse of \(\rho\) is called conductivity or specific conductance represented by \(\kappa\).
The conductivity depends upon the nature of the material (insulator, semiconductor or conductor) and the temperature of the substance.
Similarly, the conductance due to the ions present in the solution (ionic conductance) depends upon the nature of the electrolyte, size of ions, the nature of the solvent and the temperature.
Molar conductivity ( \(\Lambda_m\) ) of a solution at a given concentration is the conductance of volume \(V\) containing one mole of electrolyte kept between two electrodes of area \(A\) and unit distance apart.
It is given by the expression \(\Lambda_m=\kappa V .\)
Molar conductivity increases with decrease in concentration and when concentration approaches zero, it is called limiting molar conductivity.
The decrease is linear for a strong electrolyte. However, for a weak electrolyte the change is gradual at higher concentrations and sharp near zero concentration.
Using limiting molar conductivity values of strong electrolytes we can calculate the limiting molar conductivity of weak electrolytes using Kohlrausch law of independent migration of ions.
From molar conductivity and limiting molar conductivity we can determine the degree of dissociation \(\left(\frac{\Lambda_m}{\Lambda_m^0}\right)\) and the ionization constant of a weak acid.
Select the correct statement.