Electrostatics & Capacitors · JEE Main previous year questions

2018 9 questions

1. Q552018 · 16 Apr 2018 · Shift 1
   
   1. A.$C_{1}E[1-\exp (-tR/C_1)]$
   2. B.$C_{2}E[1-\exp (-t/R{C}_2)]$
   3. C.$C_{eq}E[1-\exp (-t/R{C}_{eq})]$
   4. D.$C_{eq}E\exp (-t/R{C}_{eq})$
   Show answer

   Answer: C

2. Q382018 · 15 Apr 2018 · Shift 1

   A body of mass $M$ and charge $q$ is connected to spring of spring constant $k$. It is oscillating along $x$-direction about its equilibrium position, taken to be at $x=0$, with an amplitude $A$. An electric field $E$ is applied along the $x$-direction. Which of the following statements is correct ?

   1. A.The new equilibrium position is at a distance $\frac{qE}{2k}$ from $x=0$.
   2. B.The total energy of the system is $\frac{1}{2}m{\omega }^2{A}^2+\frac{1}{2}\frac{q^2{E}^2}{k}$.
   3. C.The total energy of the system is $\frac{1}{2}m{\omega }^2{A}^2-\frac{1}{2}\frac{q^2{E}^2}{k}$.
   4. D.The new equilibrium position is at a distance $\frac{2qE}{k}$ from $x=0$.
   Show answer

   Answer: B

3. Q492018 · 15 Apr 2018 · Shift 1
   
   1. A.$\frac{Q}{{ϵ}_0}$
   2. B.$\frac{Q}{2{ϵ}_0}$
   3. C.$\frac{Q}{3{ϵ}_0}$
   4. D.$\frac{Q}{6{ϵ}_0}$
   Show answer

   Answer: D

4. Q532018 · 15 Apr 2018 · Shift 1

   An ideal capacitor of capacitance $0.2\mu F$ is charged to a potential difference of $10V$. The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self inductance $0.5mH$. The current at a time when the potential difference across the capacitor is $5V$, is :

   1. A.$0.34A$
   2. B.$0.25A$
   3. C.$0.17A$
   4. D.$0.15A$
   Show answer

   Answer: C

5. Q552018 · 15 Apr 2018 · Shift 1
   
   1. A.$2.4\mu F$
   2. B.$4.9\mu F$
   3. C.$3.6\mu F$
   4. D.$5.4\mu F$
   Show answer

   Answer: A

6. Q442018 · 8 Apr 2018 · Shift 1

   Three concentric metal shells A, B and C of respective radii a, b and c $(a<b<c)$ have surface charge densities $+\sigma ,-\sigma$ and $+\sigma$ respectively. The potential of shell B is :

   1. A.$\frac{\sigma }{{ϵ}_0}\left[\frac{b^2-c^2}{c}+a\right]$
   2. B.$\frac{\sigma }{{ϵ}_0}\left[\frac{a^2-b^2}{a}+c\right]$
   3. C.$\frac{\sigma }{{ϵ}_0}\left[\frac{a^2-b^2}{b}+c\right]$
   4. D.$\frac{\sigma }{{ϵ}_0}\left[\frac{b^2-c^2}{b}+a\right]$
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   Answer: C

7. Q452018 · 8 Apr 2018 · Shift 1

   A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20 V. If a dielectric material of dielectric constant K = 5/3 is inserted between the plates, the magnitude of the induced charge will be :

   1. A.0.9 n C
   2. B.1.2 n C
   3. C.0.3 n C
   4. D.2.4 n C
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   Answer: B

8. Q492018 · 8 Apr 2018 · Shift 1

   The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is $B_1$. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is $B_2$. The ratio $\frac{B_1}{B_2}$ is:

   1. A.2
   2. B.$\sqrt{3}$
   3. C.$\sqrt{2}$
   4. D.$\frac{1}{\sqrt{2}}$
   Show answer

   Answer: C

9. Q512018 · 8 Apr 2018 · Shift 1

   An EM wave from air enters a medium. The electric fields are ${\vec{E}}_1=E_{01}\hat{x}\cos \left[2\pi \nu \left(\frac{z}{c}-t\right)\right]$ in air and ${\vec{E}}_2=E_{02}\hat{x}\cos [k(2z-ct)]$ in medium, where the wave number k and frequency $\nu$ refer to their values in air. The medium is non-magnetic. If ${\epsilon }_{r_1}$ and ${\epsilon }_{r_2}$ refer to relative permittivities of air and medium respectively, which of the following options is correct ?

   1. A.$\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}}=4$
   2. B.$\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}}=2$
   3. C.$\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}}=\frac{1}{4}$
   4. D.$\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}}=\frac{1}{2}$
   Show answer

   Answer: C