The time taken for the magnetic energy to reach 25% of its maximum value, when solenoid of resistance R, inductance L is connected to a battery, is:
The time taken for the magnetic energy to reach 25% of its maximum value, when solenoid of resistance R, inductance L is connected to a battery, is:
Option 1 -
(L/R)ln(2)
Option 2 -
(L/R)ln(10)
Option 3 -
Infinite
Option 4 -
(L/R)ln(5)
Asked by Shiksha User
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1 Answer
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Correct Option - 1
Detailed Solution:I = (V/R) (1 - e^ (-t/τ) where τ = L/R
E = (1/2)LI² = (1/2)L (V²/R²) (1 - e^ (-t/τ)² ⇒ Energy stored in inductor
According to Question, we can write
(1/4) * (1/2) (LV²/R²) = (1/2) (LV²/R²) (1 - e^ (-t/τ)²
⇒ 1/4 = (1 - e^ (-t/τ)² ⇒ 1/2 = 1 - e^ (-t/τ) ⇒ e^ (-t/τ) = 1/2⇒ t/τ = ln (2) ⇒ t = τln (2) = (L/R)ln (2)
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