Figure shows a current carrying square loop ABCD of edge length 'a' lying in a plane. If the resistance of the ABC part is r and that of ADC part is 2r, then the magnitude of the resultant magnetic field at centre of the square loop is

A

$$\frac{3\pi\mu_0 I}{\sqrt{2}a}$$

B

$$\frac{\mu_0 I}{2\pi a}$$

C

$$\frac{\sqrt{2}\mu_0 I}{3\pi a}$$

D

$$\frac{2\mu_0 I}{3\pi a}$$