A coil of wire of a certain radius has 100 turns and a self inductance of 15 mH. The self inductance of a second similar coil of 500 turns will be

Question

A coil of wire of a certain radius has 100 turns and a self inductance of 15 mH. The self inductance of a second similar coil of 500 turns will be (A) 75 mH (B) 375 mH (C) 15 mH (D) none of these

Tardigrade Admin · Accepted Answer

Inductance of a coil is given by L = (1/2)μ0π N2R ⇒ (L2/L1) = (N22/N21) ∴ L2 = L1 (N22/N21) = ((500/100))2 15 mH = 375 mH

Q. A coil of wire of a certain radius has $100$ turns and a self inductance of $15 m H$ . The self inductance of a second similar coil of $500$ turns will be

75 mH

375 mH

15 mH

none of these

Inductance of a coil is given by
$L = \frac{1}{2} μ_{0} π N^{2} R$
$\Rightarrow \frac{L _{2}}{L _{1}} = \frac{N _{2}^{2}}{N _{1}^{2}}$
$∴ L_{2} = L_{1} \frac{N _{2}^{2}}{N _{1}^{2}} = (\frac{500}{100})^{2} 15 m H = 375 m H$

Q. A coil of wire of a certain radius has 100 turns and a self inductance of 15mH. The self inductance of a second similar coil of 500 turns will be