Q. No.A parallel plate air capacitor has a capacitance \(C\). When it is half filled as show in figure with a dielectric constant \(K=5\), the percentage increase in the capacitance is:
1. \(33.34\)
2. \(66.67\)
3. \(200\)
4. \(400\)
1. \(33.34\)
2. \(66.67\)
3. \(200\)
4. \(400\)
Subtopic: Dielectrics in Capacitors |
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A parallel plate capacitor has capacitance \(C\), when there is vacuum within the parallel plates. A sheet having thickness \(\left(\dfrac{1}{3}\right)^{\mathrm{rd}}\) of the separation between the plates and relative permittivity \(K\) is introduced between the plates. The new capacitance of the system is:
1. \(\dfrac{3 {KC}}{2 {K}+1}\)
2. \(\dfrac{C K}{2+K}\)
3. \(\dfrac{3 {CK}^2}{(2 {K}+1)^2}\)
4. \(\dfrac{4 {KC}}{3{K}-1}\)
1. \(\dfrac{3 {KC}}{2 {K}+1}\)
2. \(\dfrac{C K}{2+K}\)
3. \(\dfrac{3 {CK}^2}{(2 {K}+1)^2}\)
4. \(\dfrac{4 {KC}}{3{K}-1}\)
Subtopic: Dielectrics in Capacitors |
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The space between the plates of a parallel-plate capacitor of capacitance \(C\) (without any dielectric) is now filled with three dielectric slabs of dielectric constants \(K_1 =2, K_2 =3,\) and \(K_3 =5\) (as shown in the figure). If new capacitance is \(\dfrac{n}{3} \text{C}\) then the value of \(n\) is:
1. \(3\)
2. \(8\)
3. \(4\)
4. \(6\)
1. \(3\)
2. \(8\)
3. \(4\)
4. \(6\)
Subtopic: Dielectrics in Capacitors |
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A parallel plate capacitor with plate separation \(5\) mm is charged by a battery. On introducing a mica sheet of \(2\) mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws \(25\%\) more charge from the battery. The dielectric constant of mica is:
1. \(2.5\)
2. \(2.0\)
3. \(1.5\)
4. \(1.0\)
1. \(2.5\)
2. \(2.0\)
3. \(1.5\)
4. \(1.0\)
Subtopic: Dielectrics in Capacitors |
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Three parallel plate capacitors each with area \(A\) and separation \(d\) are filled with two dielectric \((k_1\) and \(k_2)\) in the following fashion. Which of the following is true? \((k_1 >~k_2)\)
1. \(C_B>C_C>C_A~\)
2. \(C_C>C_B>C_A~\)
3. \(C_C>C_A>C_B~\)
4. \(C_A>C_C>C_B~\)
1. \(C_B>C_C>C_A~\)
2. \(C_C>C_B>C_A~\)
3. \(C_C>C_A>C_B~\)
4. \(C_A>C_C>C_B~\)
Subtopic: Dielectrics in Capacitors |
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Three parallel plate capacitors \(C_1, C_2\) and \(C_3\) each of capacitance \(5 ~\mu \text{F}\) are connected as shown in figure. The effective capacitance between points \(A\) and \(B,\) when the space between the parallel plates of \(C_1\) capacitor is filled with a dielectric medium having dielectric constant of \(4,\) is:
1. \(30~\mu \text{F}\)
2. \(7.5~\mu \text{F}\)
3. \(22.5~\mu \text{F}\)
4. \(9~\mu \text{F}\)
1. \(30~\mu \text{F}\)
2. \(7.5~\mu \text{F}\)
3. \(22.5~\mu \text{F}\)
4. \(9~\mu \text{F}\)
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Space between the plates of a parallel plate capacitor of plate area \(4~\text{cm}^2\) and separation of \(d= 1.77~\text{mm},\) is filled with uniform dielectric materials with dielectric constants (\(3\) and \(5\)) as shown in figure. Another capacitor of capacitance \(7.5~\text{pF}\) is connected in parallel with it. The effective capacitance of this combination is: (in pF) (Given \(ε_0 = 8.85 × 10^{-12}~ \text{F/m}\))
1. \(15\)
2. \(19\)
3. \(45\)
4. \(30\)
1. \(15\)
2. \(19\)
3. \(45\)
4. \(30\)
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A parallel plate capacitor has charge \(5 × 10^{-6} ~\text{C}. \) A dielectric slab is inserted between the plates and almost fills the space between the plates. If the induced charge on one face of the slab is \(4 × 10^{-6}~\text{C},\) then the dielectric constant of the slab is:
1. \(5\)
2. \(2\)
3. \(4\)
4. \(8\)
1. \(5\)
2. \(2\)
3. \(4\)
4. \(8\)
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A parallel plate capacitor is filled equally (half) with two dielectrics of dielectric constants \(\varepsilon_1\) and \(\varepsilon_2\), as shown in figures. The distance between the plates is \(d \) and area of each plate is \(A\). If capacitance in first configuration and second configuration are \(C_1\) and \(C_2\) respectively, then \(C_1/C_2 \) is:
First Configuration
Second Configuration
1. \(\dfrac{\varepsilon_1 \varepsilon_2^2}{\left(\varepsilon_1+\varepsilon_2\right)^2}\)
2. \(\dfrac{\varepsilon_1 \varepsilon_2}{\varepsilon_1+\varepsilon_2}\)
3. \(\dfrac{4 \varepsilon_1 \varepsilon_2}{\left(\varepsilon_1+\varepsilon_2\right)^2}\)
4. \(\dfrac{\varepsilon_0\left(\varepsilon_1+\varepsilon_2\right)}{2} \)
First Configuration
Second Configuration
1. \(\dfrac{\varepsilon_1 \varepsilon_2^2}{\left(\varepsilon_1+\varepsilon_2\right)^2}\)
2. \(\dfrac{\varepsilon_1 \varepsilon_2}{\varepsilon_1+\varepsilon_2}\)
3. \(\dfrac{4 \varepsilon_1 \varepsilon_2}{\left(\varepsilon_1+\varepsilon_2\right)^2}\)
4. \(\dfrac{\varepsilon_0\left(\varepsilon_1+\varepsilon_2\right)}{2} \)
Subtopic: Dielectrics in Capacitors |
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A time-varying potential difference is applied between the plates of a parallel plate capacitor of capacitance \(2.5~\mu\text{F}.\) The dielectric constant of the medium between the capacitor plates is \(1.\) It produces an instantaneous displacement current of \(0.25~\mu\text{A}\) in the intervening space between the capacitor plates, the magnitude of the rate of change of the potential difference will be:
1. \(10^2~\text{V/s}\)
2. \(10~\text{V/s}\)
3. \(10^4~\text{V/s}\)
4. \(10^3~\text{V/s}\)
1. \(10^2~\text{V/s}\)
2. \(10~\text{V/s}\)
3. \(10^4~\text{V/s}\)
4. \(10^3~\text{V/s}\)
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