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JEE Main 2009
Exam
JEE Main
Year
2009
Subject
Physics
Chapter
Electromagnetic Induction

JEE Main 2009 · Physics · Electromagnetic Induction

An inductor of inductance L=400 mH and resistors of resistances R_1...

An inductor of inductance L=400mH\mathrm{L}=400 \mathrm{mH} and resistors of resistances R1\mathrm{R}_1 =2Ω=2 \Omega and R2=2ΩR_2=2 \Omega are connected to a battery of emf 12 V12 \mathrm{~V} as shown in the figure. The internal resistance of the battery is negligible. The switch SS is closed at t=0t=0. The potential drop across LL as a function of time is An inductor of inductance L=400 mH and resistors of resistances R_1 =2 and R_2=2 are connected to a battery of emf 12

Options

  1. A6e−5tV6 e^{-5 t} V
  2. B12te−3tV\frac{12}{t} e^{-3 t} V
  3. C6(1−e−t/0.2)V6\left(1-e^{-t / 0.2}\right) V
  4. D12e−5tV12 e^{-5 t} V

Correct answer

D. 12e−5tV12 e^{-5 t} V

Step-by-step solution

I1=FR1=122=6AE=Ldl2dt+R2×I2I2=I0(1−e−t/tc)⇒Io=ER2=122=6Atc=LR=400×10−32=0.2I2=6(1−e−t/0.2)\begin{aligned}& \mathrm{I}_{1}=\frac{\mathrm{F}}{\mathrm{R}_1}=\frac{12}{2}=6 \mathrm{ A}\\ & \mathrm{E}=\mathrm{L} \frac{\mathrm{dl_{2 }}}{\mathrm{dt}}+\mathrm{R}_{2} \times \mathrm{I}_{2} \\ & \mathrm{I}_{2}=\mathrm{I}_{0}\left(1-\mathrm{e}^{-\mathrm{t}/ \mathrm{t}_{\mathrm{c}}}\right) \Rightarrow \mathrm{I}_{\mathrm{o}}=\frac{\mathrm{E}}{\mathrm{R}_2}=\frac{12}{2}=6 \mathrm{ A}\\ & \mathrm{t}_{\mathrm{c}}=\frac{\mathrm{L}}{\mathrm{R}}=\frac{400 \times 10^{-3}}{2}=0.2 \\ & \mathrm{I}_{2}=6\left(1-\mathrm{e}^{-\mathrm{t}/ 0.2}\right) \end{aligned} Potential drop across L=E−R2l2=12−2×6L=E-R_2 l_2=12-2 \times 6\left(1-e^{-b t}\right)=12e−5t<imgsrc="/api/proxy−image?url=httpse^{-5 t}<img src="/api/proxy-image?url=https%3A%2F%2Ffirebasestorage.googleapis.com%2Fv0%2Fb%2Fquantrexacademy-app.firebasestorage.app%2Fo%2Fquestions%252Ffigs%252Fpyq%252Fjee_main%252FZYOu7dEZgHrmJ8UwaY3fMFFCDsYoIxPFkYXeC8CigA4.original.fullsize.png%3Falt%3Dmedia&clean=1&v=wm2" data-qx-orig-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fjee_main%2FZYOu7dEZgHrmJ8UwaY3fMFFCDsYoIxPFkYXeC8CigA4.original.fullsize.png?alt=media" data-qx-storage-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fjee_main%2FZYOu7dEZgHrmJ8UwaY3fMFFCDsYoIxPFkYXeC8CigA4.original.fullsize.png?alt=media"> \\ Directions: Question numbers 28,29 and 30 are based on the following paragraph. Two moles of helium gas are taken over the cycle A B C D A,asshowninthe, as shown in theP-T$ diagram.An inductor of inductance L=400 mH and resistors of resistances R_1 =2 and R_2=2 are connected to a battery of emf 12
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