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Q. No.From the circuit given below, the capacitance between terminals \(A\) and \(B\) shown in the circuit is: (in \(\mu\text{F}\))
(take \(C_1=C_2=C_3=1~\mu\text{F}\) and \(C_4 = 2~\mu\text{F}\))
1. \(2\)
2. \(7/2\)
3. \(7/3\)
4. \(5/2\)
(take \(C_1=C_2=C_3=1~\mu\text{F}\) and \(C_4 = 2~\mu\text{F}\))
1. \(2\)
2. \(7/2\)
3. \(7/3\)
4. \(5/2\)
Subtopic: Combination of Capacitors |
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Level 1: 80%+
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Given below are two statements:
Choose the correct answer from the options given below:
| Assertion (A): | In electrostatics, a conductor does not store any net charge inside. |
| Reason (R): | Inside the capacitor (with no dielectric medium), the free charge carriers, if placed between the plates of capacitor, experience force and drift. |
| 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. | (A) is False but (R) is True. |
Subtopic: Electrostatic Shielding |
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Level 2: 60%+
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The electric potential as a function of \(x,~y\) is given by \(V = 5(x^{2}-y^{2})~\text{V}.\) The electric field at a point \((2,3)~\text{m}\) is: (in \(\text{V/m}\))
1. \((-20 \hat{\imath}+30 \hat{\jmath})\)
2. \((20 \hat{\imath}-30 \hat{\jmath}) \)
3. \((20 \hat{\imath}+45 \hat{\jmath}) \)
4. \((-4 \hat{\imath}+6 \hat{\jmath})\)
1. \((-20 \hat{\imath}+30 \hat{\jmath})\)
2. \((20 \hat{\imath}-30 \hat{\jmath}) \)
3. \((20 \hat{\imath}+45 \hat{\jmath}) \)
4. \((-4 \hat{\imath}+6 \hat{\jmath})\)
Subtopic: Relation between Field & Potential |
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Level 1: 80%+
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A sphere of capacitance \(100~\text{pF}\) is charged to a potential of \(100~\text{V}.\) Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is \(\alpha \times 10^{-7} ~\text{J} .\) The value of \(\alpha\) is:
(combined capacitance of spheres is \(200~\text{pF}\))
1. \(5\)
2. \(\dfrac{5}{2}\)
3. \(\dfrac{7}{2}\)
4. \(\dfrac{9}{2}\)
(combined capacitance of spheres is \(200~\text{pF}\))
1. \(5\)
2. \(\dfrac{5}{2}\)
3. \(\dfrac{7}{2}\)
4. \(\dfrac{9}{2}\)
Subtopic: Energy stored in Capacitor |
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Level 1: 80%+
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A three coulomb charge moves from the point \((0,-2,-5)\) to the point \((5, 1, 2)\) in an electric field expressed as \(\vec{E}=2 x \hat{i}+3 {y}^2 \hat{j}+4 \hat{k} ~\text{N/C} .\) The work done in moving the charge is: (in J)
1. \(110\)
2. \(150\)
3. \(186\)
4. \(220\)
1. \(110\)
2. \(150\)
3. \(186\)
4. \(220\)
Subtopic: Electric Potential Energy |
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Level 2: 60%+
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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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Level 1: 80%+
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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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A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed \(V\) \(x\)
1. \(-2\)
2. \(1\)
3. \(-1\)
4. \(2\)
1. \(-2\)
2. \(1\)
3. \(-1\)
4. \(2\)
Subtopic: Energy stored in Capacitor |
Level 3: 35%-60%
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Potential energy \((V)\) versus distance \((x)~\) is given by the graph. Rank various regions as per the magnitudes of the force \((F)\) acting on a particle from high to low.
1. \({F}_{\mathrm{BC}}>{F}_{\mathrm{CD}}>{F}_{\mathrm{DE}}>{F}_{\mathrm{AB}}\)
2. \({F}_{\mathrm{CD}}>{F}_{\mathrm{AB}}>{F}_{\mathrm{BC}}>{F}_{\mathrm{DE}}\)
3. \({F}_{\mathrm{CD}}>{F}_{\mathrm{DE}}>{F}_{\mathrm{AB}}>{F}_{\mathrm{BC}}\)
4. \({F}_{\mathrm{BC}}>{F}_{\mathrm{AB}}>{F}_{\mathrm{DE}}>{F}_{\mathrm{CD}}~\)
1. \({F}_{\mathrm{BC}}>{F}_{\mathrm{CD}}>{F}_{\mathrm{DE}}>{F}_{\mathrm{AB}}\)
2. \({F}_{\mathrm{CD}}>{F}_{\mathrm{AB}}>{F}_{\mathrm{BC}}>{F}_{\mathrm{DE}}\)
3. \({F}_{\mathrm{CD}}>{F}_{\mathrm{DE}}>{F}_{\mathrm{AB}}>{F}_{\mathrm{BC}}\)
4. \({F}_{\mathrm{BC}}>{F}_{\mathrm{AB}}>{F}_{\mathrm{DE}}>{F}_{\mathrm{CD}}~\)
Subtopic: Relation between Field & Potential |
88%
Level 1: 80%+
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