Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Capacitor question

2014 · Shift 1 · Q42
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Advanced
  3. /Physics
  4. /Capacitor
  5. /2014 · Shift 1 · Q42

Capacitor question

2014 · Shift 1 · Q42

JEE AdvancedPhysicsCapacitorMultiple correct+3 / −1
A parallel plate capacitor has a dielectric slab of dielectric constant KKK between its plates that covers 1/31/31/3 of the area of its plates, as shown in the figure. The total capacitance of the capacitor is CCC while that of the portion with dielectric in between is C1.{C_1}.C1​. When the capacitor is charged, the plate area covered by the dielectric gets charge Q1{Q_1}Q1​ and the rest of the area gets charge Q2.{Q_2}.Q2​. The electric field in the dielectric is E1{E_1}E1​ and that in the other portion is E2.{E_2}.E2​. Choose the correct option/ options, ignoring edge effects. JEE Advanced 2014 Paper 1 Offline Physics - Capacitor Question 16 English
  1. A
    E1E2=1{{{E_1}} \over {{E_2}}} = 1E2​E1​​=1
  2. B
    E1E2=1K{{{E_1}} \over {{E_2}}} = {1 \over K}E2​E1​​=K1​
  3. C
    Q1Q2=3K{{{Q_1}} \over {{Q_2}}} = {3 \over K}Q2​Q1​​=K3​
  4. D
    CC1=2+KK{C \over {{C_1}}} = {{2 + K} \over K}C1​C​=K2+K​
View written solutionFree

Correct answer: A, D

  1. Model the arrangement as two capacitors in parallel

Since the dielectric slab covers only 13\dfrac{1}{3}31​ of the plate area, the capacitor is equivalent to two parallel capacitors:

  • Part 1: area A/3A/3A/3, dielectric constant KKK
  • Part 2: area 2A/32A/32A/3, air/vacuum

Both parts have the same plate separation ddd, and since they are side-by-side between the same plates, they have the same potential difference VVV.

  1. Capacitance of each part

Let total plate area be AAA.

For the dielectric-covered part,

C1=Kε0(A/3)d=Kε0A3dC_1 = \frac{K\varepsilon_0 (A/3)}{d} = \frac{K\varepsilon_0 A}{3d}C1​=dKε0​(A/3)​=3dKε0​A​

For the uncovered part,

C2=ε0(2A/3)d=2ε0A3dC_2 = \frac{\varepsilon_0 (2A/3)}{d} = \frac{2\varepsilon_0 A}{3d}C2​=dε0​(2A/3)​=3d2ε0​A​

Since they are in parallel,

C=C1+C2=Kε0A3d+2ε0A3d=(K+2)ε0A3dC = C_1 + C_2 = \frac{K\varepsilon_0 A}{3d} + \frac{2\varepsilon_0 A}{3d} = \frac{(K+2)\varepsilon_0 A}{3d}C=C1​+C2​=3dKε0​A​+3d2ε0​A​=3d(K+2)ε0​A​

Therefore,

CC1=(K+2)ε0A3dKε0A3d=K+2K\frac{C}{C_1} = \frac{\frac{(K+2)\varepsilon_0 A}{3d}}{\frac{K\varepsilon_0 A}{3d}} = \frac{K+2}{K}C1​C​=3dKε0​A​3d(K+2)ε0​A​​=KK+2​

So Option D is correct.

  1. Compare electric fields E1E_1E1​ and E2E_2E2​

Both regions are connected across the same plates, so both experience the same potential difference VVV across the same separation ddd.

Hence,

E1=Vd,E2=VdE_1 = \frac{V}{d}, \qquad E_2 = \frac{V}{d}E1​=dV​,E2​=dV​

So,

E1E2=1\frac{E_1}{E_2} = 1E2​E1​​=1

Thus Option A is correct.

So Option B is incorrect.

  1. Compare charges Q1Q_1Q1​ and Q2Q_2Q2​

Since both parts have the same voltage VVV,

Q1=C1V,Q2=C2VQ_1 = C_1 V, \qquad Q_2 = C_2 VQ1​=C1​V,Q2​=C2​V

Thus,

Q1Q2=C1C2=Kε0A3d2ε0A3d=K2\frac{Q_1}{Q_2} = \frac{C_1}{C_2} = \frac{\frac{K\varepsilon_0 A}{3d}}{\frac{2\varepsilon_0 A}{3d}} = \frac{K}{2}Q2​Q1​​=C2​C1​​=3d2ε0​A​3dKε0​A​​=2K​

This is not 3K\dfrac{3}{K}K3​.

So Option C is incorrect.

  1. Final evaluation of options
  • A: Correct
  • B: Incorrect
  • C: Incorrect
  • D: Correct

Therefore, the correct options are:

A,D\boxed{A, D}A,D​
  1. Comparison with stored answer

Stored correct answer: A, D

Derived answer: A, D

They match.

PreviousNext

More from Capacitor

  • In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance C. The switch S1​ is pressed first to fully charge the capacitor C1​ and then released. The switch S2​ is then pressed to charge… Includes diagram2013 · Multiple correct
  • In the given circuit, a charge of +80μC is given to the upper plate of the 4μF capacitor. Then in the steady state, the charge on the upper plate of the 3μF capacitor is Includes diagram2012 · MCQ
  • A 2μF capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch S is turned to position 2 is Includes diagram2011 · MCQ
  • At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them becomes 4 V? (Take ln5 = 1.6, ln3 = 1.1) Includes diagram2010 · Numerical
  • A circuit is connected as shown in the figure with the switch S open. When the switch is closed, the total amount of charge that flows from Y to X is Includes diagram2007 · MCQ
  • Column I gives certain situations in which a straight metallic wire of resistance R is used and Column II gives some resulting effects. Match the statements in Column I with the statements in Column II and indicate your answer by darkening… Includes table2007 · MCQ
  • Four identical thin, square metal sheets, S1​,S2​,S3​ and S4​, each of side a are kept parallel to each other with equal distance d(≪a) between them, as shown in the figure. Let C0​=dε0​a2​,… Includes table Includes diagram2024 · MCQ
  • In a circuit shown in the figure, the capacitor C is initially uncharged and the key K is open. In this condition, a current of 1 A flows through the 1Ω resistor. The key is closed at time t=t0​. Which of the… Includes diagram2023 · Multiple correct