Question

A coil of Cu wire (radius-r, self inductance-L) is bent in two concentric turns each having radius is $\frac{r}{2}.$ The self inductance now

• A. 2L
• B. L
• C. 4 L
• D. L2

Answer 1

Answer: (A)

2L

Answer 2

$L \propto N^{2}r$; $\frac{L_{1}}{L_{2}} = \left( \frac{N_{1}}{N_{2}} \right)^{2} \times \frac{r_{1}}{r_{2}}$

⇒ $\frac{L}{L_{2}} = \left( \frac{1}{2} \right)^{2} \times \left( \frac{r}{r/2} \right) = \frac{1}{2}$; L₂ = 2L