A metallic sphere of capacitance ${C}_{1}$, charged to electric potential ${V}_{1}$ is connected by a metal wire to another metallic sphere of capacitance ${C}_{2}$ charged to electric potential ${V}_{2}$. The amount of heat produced in the connecting wire during the process is

(1)$\frac{{C}_{1}{C}_{2}}{2\left({C}_{1}+{C}_{2}\right)}{\left({V}_{1}+{V}_{2}\right)}^{2}$

(2) $\frac{{C}_{1}{C}_{2}}{2\left({C}_{1}+{C}_{2}\right)}{\left({V}_{1}-{V}_{2}\right)}^{2}$

(3) $\frac{{C}_{1}{C}_{2}}{{C}_{1}+{C}_{2}}{\left({V}_{1}-{V}_{2}\right)}^{2}$

(4) zero

Subtopic:  Energy stored in Capacitor |
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The electric potential at the surface of a charged solid sphere of insulator is 20V. The value of electric potential at its centre will be

1.  30V

2.  20V

3.  40V

4.  Zero

Subtopic:  Electric Potential |
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The capacitance of a parallel plate capacitor is C. If a dielectric slab of thickness equal to one-fourth of the plate separation and dielectric constant K is inserted between the plates, then new capacitance become

1. $\frac{KC}{2\left(K+1\right)}$

2. $\frac{2KC}{K+1}$

3. $\frac{5KC}{4K+1}$

4. $\frac{4KC}{3K+1}$

Subtopic:  Dielectrics |
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The electric potential at a point at distance 'r' from a short dipole is proportional to

(1) ${r}^{2}$

(2) ${\mathrm{r}}^{-1}$

(3) ${r}^{-2}$

(4) ${r}^{1}$

Subtopic:  Electric Potential |
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A hollow charged metal spherical shell has radius R. If the potential difference between its surface and a point at a distance 3R from the center is V, then the value of electric field intensity at a point at distance 4R from the center is

1.  $\frac{3\mathrm{V}}{19\mathrm{R}}$

2.  $\frac{\mathrm{V}}{6\mathrm{R}}$

3.  $\frac{3\mathrm{V}}{32\mathrm{R}}$

4.  $\frac{3\mathrm{V}}{16\mathrm{R}}$

Subtopic:  Electric Potential |
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Capacitors  are connected in series across a source of emf 20KV. The potential difference across ${C}_{1}$ will be

(1) 5 KV

(2) 15 KV

(3) 10 KV

(4) 20 KV

Subtopic:  Combination of Capacitors |
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The equivalent capacitance between A and B is as the given figure:

(1) $16\mathrm{\pi }{\in }_{0}\mathrm{r}$

(2) $4\mathrm{\pi }{\in }_{0}\mathrm{r}$

(3) $8\mathrm{\pi }{\in }_{0}\mathrm{r}$

(4) None of these

Subtopic:  Combination of Capacitors |
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Two metallic spheres of radii 2cm and 3cm are given charges 6mC and 4mC respectively. The final charge on the smaller sphere will be if they are connected by a conducting wire

(1) 4mC

(2) 6mC

(3) 5mC

(4) 10mC

Subtopic:  Electric Potential |
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When a proton at rest is accelerated by a potential difference V, its speed is found to be v. The speed of an $\alpha$ particle when accelerated by the same potential difference from rest will be

(1) v

(2) $\frac{v}{\sqrt{2}}$

(3) $v\sqrt{2}$

(4) 2v

Subtopic:  Electric Potential Energy |
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In the circuit shown in figure, energy stored in 6$\mathrm{\mu F}$ capacitor will be

1.

2.

3.

4.

Subtopic:  Energy stored in Capacitor |
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Difficulty Level: