Physics - EMI/AC Question with Solution | TestHub

PhysicsEMI/ACSelf and mutual inductorHard2 minQB

PhysicsHardinteger

Passage / Comprehension

Kinetic inductance: When we calculate inductance of an inductor, it is representing the tendency of current through the inductor coil to remain constant. This is due to Faraday's law. In addition, electrons in the coil have inertia, so they also tend to move with a constant speed. So total inductance of an inductor is sum of both these effects. This kinetic inductance can be found by energy considerations. Consider an ideal solenoid of cross section radius 1 cm, length of 10 m, area of cross section of it's wires $= 1 mm^{2}$ , no. of turns/length = 1000, $n = 1 0^{28} / m^{3}$ .

Ratio of kinetic inductance and inductance is of order of $1 0^{n}$ . Find n.

Options:

Answer:

-10

Solution:

$\frac{1}{2} Li^{2} = \frac{1}{2} (L_{0} + L_{k}) i^{2} \frac{1}{2} L_{k} i^{2} = \frac{1}{2} m_{e} \times n \times A ℓ v^{2} i = neAv^{2} \frac{1}{2} L_{k} n^{2} e^{2} A^{2} v^{2} = \frac{1}{2} m_{e} nA ℓ v^{2} L_{k} = \frac{m _{e} ℓ ^{'}}{ne ^{2} A} = \frac{m _{e} 2 π R \times n _{e} ℓ}{ne ^{2} A} L = μ_{0} n_{e}^{2} A_{c} ℓ \frac{L _{k}}{L} = \frac{m _{e} \times 2 π R _{L} n _{e} ℓ}{ne ^{2} A} \times \frac{1}{μ _{0} n _{e}^{2} A _{c} ℓ} = \frac{9.1 \times 1 0 ^{- 31} \times 2 π \times 1 0 ^{- 2}}{1 0 ^{28} \times ( 1.6 \times 1 0 ^{- 19} ) ^{2} \times 1 0 ^{- 6} \times 4 π \times 1 0 ^{- 7} \times 1 0 ^{3} \times π \times 1 0 ^{- 4}} = \frac{9.1}{2 π \times 256} \times 1 0^{- 9} \approx 1 0^{- 10}$

Stream:JEESubject:PhysicsTopic:EMI/ACSubtopic:Self and mutual inductor

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...