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Q. No.A parallel-plate capacitor of area \(A\), plate separation \(d\) and capacitance \(C\) is filled with four dielectric materials having dielectric constants \(k_1, k_2,k_3\) and \(k_4\) as shown in the figure below. If a single dielectric material is to be used to have the same capacitance \(C\) in this capacitor, then its dielectric constant \(k\) is given by:
| 1. | \( {k}={k}_1+{k}_2+{k}_3+3 {k}_4\) |
| 2. | \({k}=\frac{2}{3}\left({k}_1+{k}_2+{k}_3\right)+2 {k}_4\) |
| 3. | \({k}=\frac{2}{3} {k}_4\left(\frac{{k}_1}{{k}_1+{K}_4}+\frac{{k}_2}{{k}_2+{k}_4}+\frac{{k}_3}{{k}_3+{k}_4}\right)\) |
| 4. | \(\frac{1}{{k}}=\frac{1}{{k}_1}+\frac{1}{{k}_2}+\frac{1}{{k}_3}+\frac{3}{2 {k}_4}\) |
Subtopic: Â Dielectrics in Capacitors |
 63%
From NCERT
NEET - 2016
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A dielectric slab of dielectric constant \(3\) having the same area of cross-section as that of a parallel plate capacitor but of thickness \({\frac{3}{4}}^{\text{th}}\) of the separation of the plates is inserted into the capacitor. The ratio of potential difference across the plates without dielectric to that with dielectric is:
1. \(1:2\)
2. \(2:3\)
3. \(3:2\)
4. \(2:1\)
1. \(1:2\)
2. \(2:3\)
3. \(3:2\)
4. \(2:1\)
Subtopic: Â Dielectrics in Capacitors |
 57%
From NCERT
NEET - 2024
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Two capacitors, each having a capacitance of \(40~\mu\text F\) are connected in series. The space between one of the capacitors is filled with a dielectric material of dielectric constant \(K,\) such that the equivalent capacitance of the system becomes \(24~\mu\text F.\) The value of \(K\) will be:
1. \(1.5\)
2. \(2.5\)
3. \(1.2\)
4. \(3\)
1. \(1.5\)
2. \(2.5\)
3. \(1.2\)
4. \(3\)
Subtopic: Â Dielectrics in Capacitors |
 63%
From NCERT
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Given below are two statements:
| Assertion (A): | In the absence of an externally applied electric field, the displacement per unit volume of a polar dielectric material is always zero. |
| Reason (R): | In polar dielectrics, each molecule has a permanent dipole moment, but these dipoles are randomly oriented when there is no external electric field. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
Subtopic: Â Dielectrics in Capacitors |
 81%
From NCERT
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