- 1(current)
Q. No.The left half of a parallel plate capacitor is filled with a dielectric of relative permittivity \(K\) while the right half is filled with air. The capacitor is charged by connecting its plates to a battery. The electric field within the dielectric is \(E_K\) and that within the air is \(E.\) Which, of the following, is true?
| 1. | \(E_K=E\) | 2. | \({\Large\frac{E_K}{E}}=K\) |
| 3. | \({\Large\frac{E_K}{E}}={\large\frac{1}{K}}\) | 4. | \({\Large\frac{E_K}{E}}=\sqrt K\) |
Subtopic: Â Dielectrics in Capacitors |
Level 4: Below 35%
Hints
The left plate \(A\) of an air capacitor is connected to the positive terminal while the right plate \(B\) is connected to the negative terminal of a cell of voltage \(V_0.\) Assume that the plate area is \(A,\) and the plate separation is \(d.\) If a slab of dielectric constant \(K\) is inserted into the space between the plates, the electric field in the dielectric will be: (compared to the air capacitor)
| 1. | more. |
| 2. | less. |
| 3. | equal. |
| 4. | more or less or equal depending on the value of \(K\). |
Subtopic: Â Dielectrics in Capacitors |
Level 3: 35%-60%
Hints
An arrangement consisting of two concentric spherical shells A and B has a capacitance \(C_0\) between them. If the upper 'hemispherical' space between them is filled by a dielectric of relative permittivity \(K_1\) and the lower by one of relative permittivity \(K_2,\) the new capacitance will be:
1. \(\left(K_{1}+K_{2}\right) C_{0}\)
2. \( \dfrac{K_{1}+K_{2}}{2} C_{0}\)
3. \(\dfrac{1}{2}\left(\dfrac{1}{K_{1}}+\dfrac{1}{K_{2}}\right) C_{0}\)
4. \( \dfrac{2 K_{1} K_{2}}{K_{1}+K_{2}} C_{0}\)
1. \(\left(K_{1}+K_{2}\right) C_{0}\)
2. \( \dfrac{K_{1}+K_{2}}{2} C_{0}\)
3. \(\dfrac{1}{2}\left(\dfrac{1}{K_{1}}+\dfrac{1}{K_{2}}\right) C_{0}\)
4. \( \dfrac{2 K_{1} K_{2}}{K_{1}+K_{2}} C_{0}\)
Subtopic: Â Dielectrics in Capacitors |
Level 3: 35%-60%
Hints
- 1(current)
Q. No.
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