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Q. No.A parallel plate capacitor with plate area \(A\) and plate separation \(d =2~\text{m}\) has a capacitance of \( 4~\mu\text{F}\). The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant \(K=3\) (as shown in the figure) will be:
1. \( 2~\mu\text{F}\)
2. \( 32~\mu\text{F}\)
3. \( 6~\mu\text{F}\)
4. \( 8~\mu\text{F}\)
1. \( 2~\mu\text{F}\)
2. \( 32~\mu\text{F}\)
3. \( 6~\mu\text{F}\)
4. \( 8~\mu\text{F}\)
Subtopic: Dielectrics in Capacitors |
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A parallel plate capacitor is made of two dielectric blocks in series. One of the blocks has thickness \(d_1\) and dielectric constant \(K_1\) and the other has thickness \(d_2\) and dielectric constant \(K_2\) as shown in the figure below. This arrangement can be thought as a dielectric slab of thickness \(d=(d_1+d_2)\) and effective dielectric constant \(K.\) The value of \(K\) is:
| 1. | \(\dfrac{ K_1 d_1+K_2 d_2}{d_1+d_2} \) | 2. | \( \dfrac{K_1 d_1+K_2 d_2}{K_1+K_2} \) |
| 3. | \( \dfrac{K_1 K_2\left(d_1+d_2\right)}{\left(K_1 d_2+K_2 d_1\right)} \quad \) | 4. | \( \dfrac{2 K_1 K_2}{K_1+K_2}\) |
Subtopic: Dielectrics in Capacitors |
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As shown in the figure, a parallel plate condenser is filled with two dielectrics. The area of each plate is \(A\) m2 and the separation between the plates is \(d\) metre. The dielectric constants are \(K_1\) and \(K_2\) respectively. The capacitance in farad, between \(\mathrm{A}\) and \(\mathrm{B},\) will be:
1. \(\frac{\varepsilon_0A}{d}(K_1+K_2)\)
2. \(\frac{\varepsilon_0A}{2d}(K_1+K_2)\)
3. \(\frac{\varepsilon_0A}{d}2(K_1+K_2)\)
4. \(\frac{\varepsilon_0A}{2d}2(K_1-K_2)\)
1. \(\frac{\varepsilon_0A}{d}(K_1+K_2)\)
2. \(\frac{\varepsilon_0A}{2d}(K_1+K_2)\)
3. \(\frac{\varepsilon_0A}{d}2(K_1+K_2)\)
4. \(\frac{\varepsilon_0A}{2d}2(K_1-K_2)\)
Subtopic: Dielectrics in Capacitors |
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A pair of parallel plates of surface area \(A\) are placed at a small distance \(d\) from each other. If a dielectric of dielectric constant \(K\) is inserted between the plates, the capacitance is:
1. \(\dfrac{\varepsilon_0A}{d}\)
2. \(\dfrac{K\varepsilon_0A}{d}\)
3. \(\dfrac{\varepsilon_0A}{K~d}\)
4. \(\dfrac{(K+1)\varepsilon_0A}{d}\)
1. \(\dfrac{\varepsilon_0A}{d}\)
2. \(\dfrac{K\varepsilon_0A}{d}\)
3. \(\dfrac{\varepsilon_0A}{K~d}\)
4. \(\dfrac{(K+1)\varepsilon_0A}{d}\)
Subtopic: Dielectrics in Capacitors |
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A dielectric slab with a dielectric constant \(K\) has the same cross-sectional area as the plates of a parallel plate capacitor and a thickness of \(\dfrac{3}{4}d,\) where \(d\) is the separation between the plates. What will be the capacitance of the capacitor when the slab is inserted between the plates? (where \(C_{0}\) is the capacitance of the capacitor with air as the medium between the plates)
| 1. | \(\dfrac{4KC_0}{3+K}\) | 2. | \(\dfrac{3KC_0}{3+K}\) |
| 3. | \(\dfrac{3+K}{4KC_0}\) | 4. | \(\dfrac{K}{4+K}\) |
Subtopic: Dielectrics in Capacitors |
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A parallel plate capacitor with air between the plates has a capacitance of \(8~p\text{F}.\). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant \(6?\)
1. \(48~p\text{F}\)
2. \(8~p\text{F}\)
3. \(96~p\text{F}\)
4. \(60~p\text{F}\)
Subtopic: Dielectrics in Capacitors |
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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: Dielectrics in Capacitors |
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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 |
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AIPMT - 2014
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A parallel plate condenser has a capacitance 50 μF in air and 110 μF when immersed in an oil. The dielectric constant ‘k’ of the oil is
1. 0.45
2. 0.55
3. 1.10
4. 2.20
Subtopic: Dielectrics in Capacitors |
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