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QJEEM19Ph3065: JEE Main 2019 Physics - Class 12 JEEM19Ph3065 Solution: A 20 Henry inductor coil is connected to a 10 ohm resistance in …

A 20 Henry inductor coil is connected to a 10 ohm resistance in series as shown in figure. The time at which rate of dissipation of energy (joule's heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor is : JEE Main 2019 (Online) 8th April Morning Slot Physics - Electromagnetic Induction Question 98 English

Multiple Choice Options

  • A 2ln⁡2{2 \over {\ln 2}}
  • B ln⁡2{\ln 2}
  • C 2ln⁡22{\ln 2}
  • D 12ln⁡2{1 \over 2}{\ln 2}

Step-by-Step Verified Solution

PR = i2 × R

PB = V × i

∴\therefore PL = Vi – i2R

⇒\Rightarrow Vi – i2R = i2R

⇒\Rightarrow i=V2R  and  i=VR(1−e−t/τ)i = {V \over {2R}}\,\,and\,\,i = {V \over R}\left( {1 - {e^{ - t/\tau }}} \right)

∴\therefore V2R=VR(1−e−t/τ){V \over {2R}} = {V \over R}\left( {1 - {e^{ - t/\tau }}} \right)

⇒\Rightarrow t = τ\tau ln(2) = 2010ln(2)=2ln(2){{20} \over {10}}ln(2) = 2ln(2)

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