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Test-16 (Electrostatic Potential & Capacitance)
Q. No.

The capacitance of the system (shown in the figure below) of parallel conducting plates, between the two outer plates \((X)\) and the inner plate \((Y)\) is (plate area=\(A,\) plate separation \(d,2d:\) small)
            
1. \(\dfrac{3\varepsilon_0A}{2d}\)

2. \(\dfrac{4\varepsilon_0A}{3d}\)

3. \(\dfrac{\varepsilon_0A}{3d}\)

4. \(\dfrac{\varepsilon_0A}{2d}\)

Subtopic:  Combination of Capacitors |
 72%
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The potential on the surface of a uniform spherical volume charge distribution is \(10~\text{V}\); and it is observed that the potential at its centre is \(15~\text{V}\). If the radius of the sphere is halved, keeping the total charge constant, then the potential at its centre will be:
1. \(15~\text{V}\) 2. \(30~\text{V}\)
3. \(60~\text{V}\) 4. \(120~\text{V}\)
Subtopic:  Electric Potential |
 70%
From NCERT

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Three charges are placed at the three corners of an equilateral triangle as shown in the figure. The potential at the mid-point of a side with opposite charges is \(2~\text V.\) The potential at the centre of the triangle is:
1. \(2~\text V\) 2. \(3~\text V\)
3. \(2\sqrt3~\text V\) 4. \(\dfrac{2}{\sqrt3}~\text V\)
Subtopic:  Electric Potential |
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The capacitance of the system of capacitors connected in the circuit, between \(A\) and \(B,\) equals:
                
1. \(4~\mu\)F 2. \(2.5~\mu \)F
3. \(2.4~\mu \)F 4. \(1.5~\mu \)F
Subtopic:  Combination of Capacitors |
 67%
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The capacitance of a system of concentric conducting spherical shells is \(2~\mu\text F.\) If the radii of both the shells are doubled, then the capacitance of the system will be:
1. \(8~\mu\text F\) 2. \(4~\mu\text F\)
3. \(1~\mu\text F\) 4. \(0.5~\mu\text F\)
Subtopic:  Capacitance |
 64%
From NCERT

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Consider an electric field of the form: \(\vec E=K(y\hat i+x\hat j)\)
where \(K\) is a constant, and \(x,y\) are the coordinates.
Statement I: If a charged particle is taken along the \(x\)-axis, no work will be done by the electric field.
Statement II: This electric field is conservative in nature i.e. it can be derived from a potential: \(V(x,y)=C-Kxy\)
 
1. Statement I is incorrect and Statement II is correct.
2. Both Statement I and Statement II are correct.
3. Both Statement I and Statement II are incorrect.
4. Statement I is correct and Statement II is incorrect.
Subtopic:  Relation between Field & Potential |
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The capacitance between a pair of identical conducting parallel plates \((A~\&~B),\) placed close together, is \(20\) nF (Fig I). An identical third conducting plate \((C)\) is placed parallel to the other two (Fig. II), so that they form an equidistant system of parallel plates. Plates \(A,C\) are connected by a conducting wire. The capacitance between \(A,B\) is now:
1. \(10\) nF 2. \(20\) nF
3. \(40\) nF 4. none of the above
Subtopic:  Combination of Capacitors |
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The potential on the surface of a spherical region varies from \(2\) V to \(4\) V from point to point. There are no charges in the interior of the region.
Assertion (A): The potential at the centre cannot be \(0\) V.
Reason (R): Potential in the interior of a sphere must always be greater than the potential on the surface.
 
1. (A) is True but (R) is False.
2. (A) is False but (R) is True.
3. Both (A) and (R) are True and (R) is the correct explanation of (A).
4. Both (A) and (R) are True but (R) is not the correct explanation of (A).
Subtopic:  Electric Potential |
 63%
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Three capacitors are connected in the configuration shown, with \(C_1=C_3=C\) and \(C_2=2C.\) If a charge \(Q\) is passed through the circuit from \(A\) to \(B\) (with the capacitors initially uncharged), the energies stored in the capacitors, \(C_1,C_2,C_3\) are in the ratio:
1. \(1:2:1\) 2. \(1:\dfrac12:1\)
3. \(1:4:1\) 4. \(1:\dfrac14:1\)
Subtopic:  Energy stored in Capacitor |
 65%
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A capacitance is formed by connecting two metallic balls of radius \(r\) by a conducting wire, and two oppositely charged identical metallic hemispheres \((A,B)\) slightly larger than the balls. The separation between the hemispheres and the respective balls is \(d.\) The capacitance between \(A,B\) is:
1. \(\dfrac{4\pi\varepsilon_0r^2}{d}\) 2. \(\dfrac{2\pi\varepsilon_0r^2}{d}\)
3. \(\dfrac{\pi\varepsilon_0r^2}{d}\) 4. \(\dfrac{\pi\varepsilon_0r^2}{2d}\)
Subtopic:  Capacitance |
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Test-16 (Electrostatic Potential & Capacitance)
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