Two circular coils made from same wire but radius of 1^ st coil is twice that of 2^ nd coil. If magnetic field at their centres is same then ratio of potential difference applied across them is (1^ st . to 2^ nd coil)

Step-by-step solution

Magnetic fields at the centre of the coils are equal. ₀ I₁ 2 r₁ = ₀ I₂ 2 r₂ I ₁ I ₂ = r ₁ r ₂ = 2 r r ....(given r₁=2 r₂ ) I ₁ I ₂ =2 ...(ii) The resistance through the coil, R l Here, l=2 r R ₁ R ₂ = 2 r ₁ 2 r ₂ =2 ...(ii) V ₁ ~V ₂ = I ₁ R ₁ I ₂ R ₂ =2 2=4 [From (i) and (ii)]