Inductance of a coil with turns is 10 mH and it is connected to a dc source of 10 V with internal resistance of . The energy density in the inductor when the current reaches of its maximum value is . The value of is ________. .

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Solution

Q.
Inductance of a coil with $10^{4}$ turns is 10 mH and it is connected to a dc source of 10 V with internal resistance of $10 Ω$ . The energy density in the inductor when the current reaches $(\frac{1}{e})$ of its maximum value is $α π \times \frac{1}{e^{2}} {J/m}^{3}$ . The value of $α$ is ________. $(μ_{0} = 4 π \times 10^{- 7} Tm/A)$ . [2026]

Ans.
(20)

$L = 10 \times 10^{- 3} H$

$N = 10^{4}$

$I_{0} = \frac{10}{10} = 1 A (max current)$

$I = \frac{1}{e}$

$E_{d} = \frac{B^{2}}{2 μ_{0}}$

$B = μ_{0} n I$

$L = μ_{0} n^{2} π R^{2} ℓ$

$E_{d} = \frac{μ_{0} n^{2} I^{2}}{2}$

$= \frac{4 π \times 10^{- 7} \times 10^{8} \times \frac{1}{e^{2}}}{2}$

$= \frac{20 π}{e^{2}}$

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