Q. No.A parallel plate capacitor is having separation between plates \(0.885~\text{mm}\). It has a capacitance of \(1 ~\mu \text{F}\) \(1\times10^{13}~\Omega \text{m}\) \(\alpha\times10^{7}\) \(\alpha\)
(Take permittivity of free space\(=8.85 \times 10^{-12} ~\text{F/m} \)
1. \(4\)
2. \(3\)
3. \(1\)
4. \(2\)
(Take permittivity of free space
1. \(4\)
2. \(3\)
3. \(1\)
4. \(2\)
Subtopic: Capacitance |
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Level 3: 35%-60%
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The stored charge in the capacitor in steady state of the following circuit is: (in \(\mu \text{C}\))
1. \(300\)
2. \(200\)
3. \(700\)
4. \(500\)
1. \(300\)
2. \(200\)
3. \(700\)
4. \(500\)
Subtopic: Capacitance |
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Level 1: 80%+
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The charge stored by the capacitor \(C~\) in the given circuit in the steady state is: (in \(\mu\text{C}~\))
1. \(12.5\)
2. \(10\)
3. \(7.5\)
4. \(5\)
1. \(12.5\)
2. \(10\)
3. \(7.5\)
4. \(5\)
Subtopic: Capacitance |
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A capacitor \(P\) with capacitance \(10 \times 10^{-6} ~\text{F}\) is fully charged with a potential difference of \(6.0~\text{V}\) and disconnected from the battery. The charged capacitor \(P\) is connected across another capacitor \(Q\) with capacitance \(20 \times 10^{-6} ~\text{F}.\) The charge on capacitor \(Q\) when equilibrium is established will be \(\alpha \times 10^{-5}~\text{C}\) (assume capacitor \(Q\) does not have any charge initially), the value of \(\alpha\) is:
1. \(2\)
2. \(4\)
3. \(6\)
4. \(10\)
1. \(2\)
2. \(4\)
3. \(6\)
4. \(10\)
Subtopic: Capacitance |
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Identify the correct statements:
Choose the correct answer from the options given below.
1. \(\mathrm{A,B~\text{and}~C}~\text{only}\)
2. \(\mathrm{C~\text{and}~D}~\text{only}\)
3. \(\mathrm{A,C~\text{and}~D}~\text{only}\)
4. \(\mathrm{B~\text{and}~D}~\text{only}\)
| \(\mathrm{A}.\) | Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination. |
| \(\mathrm{B}.\) | When a dielectric medium is placed between the charged plates of a capacitor, displacement of charges cannot occur due to insulation property of dielectric. |
| \(\mathrm{C}.\) | Increasing of area of capacitor plate or decreasing of thickness of dielectric is an alternate method to increase the capacitance. |
| \(\mathrm{D}.\) | For a point charge, concentric spherical shells centered at the location of the charge are equipotential surfaces. |
1. \(\mathrm{A,B~\text{and}~C}~\text{only}\)
2. \(\mathrm{C~\text{and}~D}~\text{only}\)
3. \(\mathrm{A,C~\text{and}~D}~\text{only}\)
4. \(\mathrm{B~\text{and}~D}~\text{only}\)
Subtopic: Capacitance |
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Using a battery, a \(100 ~\text{pF}\) capacitor is charged to \(60 ~\text V\) and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is \(20 ~\text V,\) its capacitance is: (in \(\text{pF}\) )
1. \(600\)
2. \(200\)
3. \(400\)
4. \(100\)
1. \(600\)
2. \(200\)
3. \(400\)
4. \(100\)
Subtopic: Capacitance |
Level 4: Below 35%
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At steady state, the charge on the capacitor, as shown in the circuit below, is:
1. \(16~\mu\text C\)
2. \(32~\mu\text C\)
3. \(27~\mu\text C\)
4. \(11~\mu\text C\)
1. \(16~\mu\text C\)
2. \(32~\mu\text C\)
3. \(27~\mu\text C\)
4. \(11~\mu\text C\)
Subtopic: Capacitance |
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A parallel plate capacitor consisting of two circular plates of radius \(10~\text{cm}\) is being charged by a constant current of \(0.15 ~\text A.\) If the rate of change of potential difference between the plates is \(7×10^8~\text{V/s} \) then the integer value of the distance between the parallel plates is: (in \(μ\text{m}\)) (Take, \(\varepsilon_0=9 \times 10^{-12} ~\text{F/m}\)) \(\pi=22 / 7 \))
1. \(1320\)
2. \(1220\)
3. \(1120\)
4. \(1020\)
1. \(1320\)
2. \(1220\)
3. \(1120\)
4. \(1020\)
Subtopic: Capacitance |
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A parallel plate capacitor was made with two rectangular plates, each with a length of \(l = 3~\text{cm}\) and breath of \(b = 1~\text{cm}.\) The distance between the plates is \(3 \mu\text{m}.\) Out of the following, which are the ways to increase the capacitance by a factor of \(10?\)
Choose the correct answer from the options given below:
1. (C) only
2. (A) only
3. (B) and (D) only
4. (C) and( E) only
| (A). | \(l = 30~\text{cm}, b = 1~ \text{cm}, d = 1 ~\mu \text{m}\) |
| (B). | \(l = 3~ \text{cm}, b = 1~ \text{cm}, d = 30 ~\mu \text{m}\) |
| (C). | \(l = 6~ \text{cm}, b = 5~ \text{cm}, d = 3 ~\mu \text{m}\) |
| (D). | \(l = 1~\text{cm}, b = 1~ \text{cm}, d = 10 ~\mu \text{m}\) |
| (E). | \(l = 5~\text{cm}, b = 2~ \text{cm}, d = 1 ~\mu\text{m}\) |
Choose the correct answer from the options given below:
1. (C) only
2. (A) only
3. (B) and (D) only
4. (C) and( E) only
Subtopic: Capacitance |
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A capacitor \(C_1=6 ~\mu\text{F}\) is charged to a potential difference of \(V_0=5~\text{V}\) using a \(5~\text V\) battery. The battery is removed and another capacitor, \(C_2=12 ~\mu \text{F}\) is inserted in place of the battery. When the switch \(S\) is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges (\(q_1\) and \(q_2\)) on the capacitors \(C_1\) and \(C_2\) when equilibrium condition is reached.
1. \({q}_1=10~ \mu \text{C}, {~q}_2=20~ \mu \text{C} ~\)
2. \(q_1=30 ~\mu \text{C},~ q_2=15~ \mu \text{C}~\)
3. \(q_1=20~ \mu\text{C},~ q_2=10~ \mu \text{C}~\)
4. \({q}_1=15~ \mu \text{C}, ~{q}_2=30~ \mu \text{C}~\)
1. \({q}_1=10~ \mu \text{C}, {~q}_2=20~ \mu \text{C} ~\)
2. \(q_1=30 ~\mu \text{C},~ q_2=15~ \mu \text{C}~\)
3. \(q_1=20~ \mu\text{C},~ q_2=10~ \mu \text{C}~\)
4. \({q}_1=15~ \mu \text{C}, ~{q}_2=30~ \mu \text{C}~\)
Subtopic: Capacitance |
Level 4: Below 35%
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