A parallel plate air capacitor of capacitance \(C\) is connected to a cell of emf \(V\) and then disconnected from it. A dielectric slab of dielectric constant \(K,\) which can just fill the air gap of the capacitor is now inserted in it. Which of the following is incorrect?

1. the potential difference between the plates decreases \(K\) times.
2. the energy stored in the capacitor decreases \(K\) times.
3. the change in energy stored is \(\frac{1}{2}CV^{2}\left ( \frac{1}{K} -1\right )\)
4. the charge on the capacitor is not conserved.

Subtopic:  Energy stored in Capacitor |
 71%
From NCERT
NEET - 2015
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Two thin dielectric slabs of dielectric constants \(K_1\) and \(K_2\) \((K_1<K_2)\) are inserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field \('E'\) between the plates with distance \('d'\) as measured from the plate \(P\) is correctly shown by: 

   
1. 2.
3. 4.
Subtopic:  Dielectrics in Capacitors |
 77%
From NCERT
AIPMT - 2014
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A conducting sphere of the radius \(R\) is given a charge \(Q.\) The electric potential and the electric field at the centre of the sphere respectively are:

1. zero and \(\frac{Q}{4 \pi \varepsilon_0 {R}^2}\) 2. \(\frac{Q}{4 \pi \varepsilon_0 R}\) and zero
3. \(\frac{Q}{4 \pi \varepsilon_0 R}\) and \(\frac{Q}{4 \pi \varepsilon_0{R}^2}\) 4. both are zero
Subtopic:  Electric Potential |
 83%
From NCERT
AIPMT - 2014
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\(A\), \(B\) and \(C\) are three points in a uniform electric field. The electric potential is: 

     
1. maximum at \(B\)
2. maximum at \(C\)
3. same at all the three points \(A, B\) and \(C\)
4. maximum at \(A\)
Subtopic:  Relation between Field & Potential |
 84%
From NCERT
AIPMT - 2013
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An electric dipole of moment \(p\) is placed in an electric field of intensity \(E.\) The dipole acquires a position such that the axis of the dipole makes an angle \(\theta\) with the direction of the field. Assuming that the potential energy of the dipole to be zero when \(\theta = 90^{\circ}\), the torque and the potential energy of the dipole will respectively be:
1. \(pE\text{sin}\theta, ~-pE\text{cos}\theta\)
2. \(pE\text{sin}\theta, ~-2pE\text{cos}\theta\)
3. \(pE\text{sin}\theta, ~2pE\text{cos}\theta\)
4. \(pE\text{cos}\theta, ~-pE\text{sin}\theta\)

Subtopic:  Energy of Dipole in an External Field |
 81%
From NCERT
AIPMT - 2012
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Four-point charges \(-Q, -q, 2q~\text{and}~2Q\) are placed, one at each corner of the square. The relation between \(Q\) and \(q\) for which the potential at the center of the square is zero is:

1. \(Q= -q\) 2. \(Q= -2q\)
3. \(Q= q\) 4. \(Q= 2q\)
Subtopic:  Electric Potential |
 75%
From NCERT
AIPMT - 2012
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A parallel plate condenser has a uniform electric field \(E\) (V/m) in the space between the plates. If the distance between the plates is \(d\) (m) and the area of each plate is \(A\) (m2), the energy (joule) stored in the condenser is:
1. \( \frac{1}{2}\varepsilon_0{E}^2 \)
2. \( \frac{{E}^2 {Ad}}{\varepsilon_0} \)
3. \( \frac{1}{2}\varepsilon_0 E^2 Ad \)
4. \(\varepsilon_0 EAd \)

Subtopic:  Energy stored in Capacitor |
 90%
From NCERT
NEET - 2021
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Four electric charges \(+ q,\) \(+ q,\) \(- q\) and \(- q\) are placed at the corners of a square of side \(2L\) (see figure). The electric potential at point \(A\), mid-way between the two charges \(+ q\) and \(+ q\) is:
              
1. \(\frac{1}{4 \pi\varepsilon_{0}} \frac{2 q}{L} \left(1 + \frac{1}{\sqrt{5}}\right)\)
2. \(\frac{1}{4 \pi\varepsilon_{0}} \frac{2 q}{L} \left(1 - \frac{1}{\sqrt{5}}\right)\)
3. zero
4. \(\frac{1}{4 \pi \varepsilon_{0}} \frac{2 q}{L} \left(1 + \sqrt{5}\right)\)

Subtopic:  Electric Potential |
 73%
From NCERT
AIPMT - 2011
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A series combination of n1 capacitors, each of value C1, is charged by a source of potential difference 4V. When another parallel combination of n2 capacitors, each of value C2, is charged by a source of potential difference V, it has the same (total) energy stored in it, as the first combination has. The value of C2, in terms of C1, is then:

1. 2C1n1n2

2. 16n2n1C1

3. 2n2n1C1

4. 16C1n1n2

Subtopic:  Energy stored in Capacitor |
 73%
From NCERT
AIPMT - 2010
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Three concentric spherical shells have radii \(a,b, ~\text{and}~c\) \((a<b<c)\) and have surface charge densities \(\sigma, -\sigma, ~\text{and}~\sigma\) respectively. If \(V_A, V_B~\text{and}~V_C\) denote the potential of the three shells, and \(c= a+b\), it can be concluded that:
1. \(\mathrm{V}_{\mathrm{C}}=\mathrm{V}_{\mathrm{A}} \neq \mathrm{V}_{\mathrm{B}}\)
2. \(\mathrm{V}_{\mathrm{C}}=\mathrm{V}_B \neq \mathrm{V}_{\mathrm{A}}\)
3. \(\mathrm{V}_{\mathrm{C}} \neq \mathrm{V}_B \neq \mathrm{V}_A\)
4. \(\mathrm{V}_{\mathrm{C}}=\mathrm{V}_B=\mathrm{V}_A\)

Subtopic:  Electric Potential |
From NCERT
AIPMT - 2009
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