All STD 12 - Electric potential and capacitance questions
Newest firstShowing 151–200 of 233 questions
- 151. The material filled between the plates of a parallel plate capacitor has resistivity \(200 \Omega \, {m}\). The value of capacitance of the capacitor is \(2\, {pF}\). If a potential difference of \(40 \,{V}\) is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is (given the value of relative permitivity of material is \(50\) ) 2021 Hard
- 152. The two thin coaxial rings, each of radius \('a'\) and having charges \(+{Q}\) and \(-{Q}\) respectively are separated by a distance of \('s'.\) The potential difference between the centres of the two rings is : 2021 Hard
- 153. Three capacitors \({C}_{1}=2\, \mu {F}, {C}_{2}=6 \, \mu {F}\) and \({C}_{3}=12 \, \mu {F}\) are connected as shown in figure. Find the ratio of the charges on capacitors \({C}_{1}, {C}_{2}\) and \({C}_{3}\) respectively:
2021 Hard - 154. Two capacitors of capacities \(2 {C}\) and \({C}\) are joined in parallel and charged up to potential \({V}\). The battery is removed and the capacitor of capacity \(C\) is filled completely with a medium of dielectric constant \({K}\). The potential difference across the capacitors will now be 2021 Medium
- 155. Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be 2021 Medium
- 156. A \(10\, \mu F\) capacitor is fully charged to a potential difference of \(50\, V\). After removing the source voltage it is connected to an uncharged capacitor in parallel. Now the potential difference across them becomes \(20\, V\). The capacitance of the second capacitor is......\(\mu F\) 2020 Hard
- 157. A \(5\, \mu F\) capacitor is charged fully by a \(220\,V\) supply. It is then disconnected from the supply and is connected in series to another uncharged \(2.5\;\mu F\) capacitor. If the energy change during the charge redistribution is \(\frac{ X }{100} \;J\) then value of \(X\) to the nearest integer is\(.....\) 2020 Medium
- 158. A \(60\; pF\) capacitor is fully charged by a \(20\; \mathrm{V}\) supply. It is then disconnected from the supply and is connected to another uncharged \(60 \;pF\) capactior is parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in \(nJ\)) 2020 Medium
- 159. A capacitor \(C\) is fully charged with voltage \(V _{0}\) After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance \(\frac{ C }{2} .\) The energy loss in the process after the charge is distributed between the two capacitors is\(.........\)\(CV _{0}^{2}\) 2020 Hard
- 160. A capacitor is made of two square plates each of side \(a\) making a very small angle \(\alpha\) between them, as shown in figure. The capacitance will be close to
2020 Hard - 161. A parallel plate capacitor has plate of length \('l',\) width \('w'\) and separation of plates is \('d'.\) It is connected to a battery of emf \(V\). A dielectric slab of the same thickness '\(d\)' and of dielectric constant \(k =4\) is being inserted between the plates of the capacitor. At what length of the slab inside plates, will be energy stored in the capacitor be two times the initial energy stored\(?\) 2020 Hard
- 162. A parallel plate capacitor has plates of area \(A\) separated by distance \(d\) between them. It is filled with a dielectric which has a dielectric constant that varies as \(\mathrm{k}(\mathrm{x})=\mathrm{K}(1+\alpha \mathrm{x})\) where \(\mathrm{x}\) is the distance measured from one of the plates. If \((\alpha \text {d)}<<1,\) the total capacitance of the system is best given by the expression 2020 Hard
- 163. A particle of charge \(q\) and mass \(m\) is subjected to an electric field \(E = E _{0}\left(1- ax ^{2}\right)\) in the \(x-\)direction, where \(a\) and \(E _{0}\) are constants. Initially the particle was at rest at \(x=0 .\) Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is 2020 Hard
- 164. A solid sphere of radius \(R\) carries a charge \((Q+q)\) distributed uniformly over its volume. A very small point like piece of it of mass \(m\) gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge \(q.\) If it acquires a speed \(v\) when it has fallen through a vertical height \(y\) (see figure), then : (assume the remaining portion to be spherical).
2020 Hard - 165. A two point charges \(4 q\) and \(-q\) are fixed on the \(x-\)axis at \(x=-\frac{d}{2}\) and \(x=\frac{d}{2},\) respectively. If a third point charge \('q'\) is taken from the origin to \(x = d\) along the semicircle as shown in the figure, the energy of the charge will
2020 Hard - 166. Concentric metallic hollow spheres of radii \(R\) and \(4 R\) hold charges \(Q _{1}\) and \(Q _{2}\) respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference \(V ( R )- V (4 R )\) is 2020 Medium
- 167. Consider two charged metallic spheres \(S_{1}\) and \(\mathrm{S}_{2}\) of radii \(\mathrm{R}_{1}\) and \(\mathrm{R}_{2},\) respectively. The electric \(\left.\text { fields }\left.\mathrm{E}_{1} \text { (on } \mathrm{S}_{1}\right) \text { and } \mathrm{E}_{2} \text { (on } \mathrm{S}_{2}\right)\) on their surfaces are such that \(\mathrm{E}_{1} / \mathrm{E}_{2}=\mathrm{R}_{1} / \mathrm{R}_{2} .\) Then the ratio \(\left.\mathrm{V}_{1}\left(\mathrm{on}\; \mathrm{S}_{1}\right) / \mathrm{V}_{2} \text { (on } \mathrm{S}_{2}\right)\) of the electrostatic potentials on each sphere is 2020 Medium
- 168. Effective capacitance of parallel combination of two capacitors \(\mathrm{C}_{1}\) and \(\mathrm{C}_{2}\) is \(10\; \mu \mathrm{F}\). When these capacitors are individually connected to a voltage source of \(1\; \mathrm{V},\) the energy stored in the capacitor \(\mathrm{C}_{2}\) is \(4\) times that of \(\mathrm{C}_{1}\). If these capacitors are connected in series, their effective capacitance will be 2020 Medium
- 169. Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to...... 2020 Medium
- 170. In the circuit shown, charge on the \(5\, \mu F\) capacitor is\(........\mu C\)
2020 Hard - 171. In the circuit shown in the figure, the total charge in \(750\, \mu C\) and the voltage across capacitor \(C _{2}\) is \(20\, V\). Then the charge on capacitor \(C _{2}\) is\(....\mu C\)
2020 Medium - 172. Ten charges are placed on the circumference of a circle of radius \(R\) with constant angular separation between successive charges. Alternate charges \(1,3,5,7,9\) have charge \((+q)\) each, while \(2,4,6,8,10\) have charge \((-q)\) each. The potential \(V\) and the electric field \(E\) at the centre of the circle are respectively (Take \(V =0\) at infinity \()\) 2020 Hard
- 173. Two capacitors of capacitances \(C\) and \(2\, C\) are charged to potential differences \(V\) and \(2\, V\), respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is\(.....CV^2\) 2020 Hard
- 174. Two identical electric point dipoles have dipole moments \(\overrightarrow{p}_{1}= p\hat i\) and \(\overrightarrow{p}_{2}=- p\hat i\) and are held on the \(x-\)axis at distance \('a'\) from each other. When released, they move along the \(x-\)axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is \('m',\) their speed when they arc infinitely far apart is 2020 Medium
- 175. Two isolated conducting spheres \(S_{1}\) and \(S_{2}\) of radius \(\frac{2}{3} R\) and \(\frac{1}{3} R\) have \(12\, \mu C\) and \(-3\, \mu C\) charges, respectively, and are at a large distance from each other. They are now onnected by a conducting wire. A long time after this is done the charges on \(S_{1}\) and \(S_{2}\) are respectively 2020 Hard
- 176. A capacitor with capacitance \(5\,\mu F\) is charged to \(5\,\mu C.\) If the plates are pulled apart to reduce the capacitance to \(2\,\mu F,\) how much work is done? 2019 Medium
- 177. A charge \(Q\) is distributed over three concentric spherical shell of radii \(a, b, c (a < b < c)\) such that their surface charge densities are equal to one another. The total potential at a point at distance \(r\) from their common centre, where \(r < a\), would be 2019 Hard
- 178. A parallel palate capacitor with square plates is filled with four dielectrics of dielectric constants \(K_1, K_2, K_3, K_4\) arranged as shown in the figure. The effective dielectric constant \(K\) will be
2019 Hard - 179. A parallel plate capacitor has \(1\,\mu F\) capacitance. One of its two plates is given \(+2\,\mu C\) charge and the other plate, \(+4\,\mu C\) charge. The potential difference developed across the capacitor is......\(V\) 2019 Medium
- 180. A parallel plate capacitor having capacitance \(12\, pF\) is charged by a battery to a potential difference of \(10\, V\) between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant \(6.5\) is slipped between the plates. The work done by the capacitor on the slab is.......\(pJ\) 2019 Hard
- 181. A parallel plate capacitor is made of two square plates of side \(a\), separated by a distance \(d\,(d < < a)\). The lower triangular portion is filled with a dielectric of dielectric constant \(K\), as shown in the figure. Capacitance of this capacitor is
2019 Hard - 182. A parallel plate capacitor is of area \(6\, cm^2\) and a separation \(3\, mm\). The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants \(K_1 = 10, K_2 = 12\) and \(K_3 = 14\). The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be
2019 Hard - 183. A parallel plate capacitor with plates of area \(1\,m^2\) each, are at a separation of \(0.1\,m.\) If the electric field between the plates is \(100\,N/C,\) the magnitude of charge on each plate 2019 Medium
- 184. A point dipole \(\vec p = - {p_0}\hat x\) is kept at the origin. The potential and electric field due to this dipole on the \(y-\) axis at a distance \(d\) are, respectively : (Take \(V = 0\) at infinity) 2019 Medium
- 185. A positive point charge is released from rest at a distance \(r_0\) from a positive line charge with uniform density. The speed \((v)\) of the point charge, as a function of instantaneous distance \(r\) from line charge, is proportional to
2019 Hard - 186. A simple pendulum of length \(L\) is placed between the plates of a parallel plate capacitor having electric field \(E,\) as shown in figure. Its bob has mass \(m\) and charge \(q.\) the time period of the pendulum is given by
2019 Hard - 187. A solid conducting sphere, having a charge \(Q\), is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be \(V\). If the shell is now given a charge of \(-4\, Q\), the new potential difference between the same two surface is......\(V\) 2019 Hard
- 188. A system of three charges are placed as shown in the figure. If \(D > > d,\) the potential energy of the system is best given \(b\)
2019 Hard - 189. A uniformly charged ring of radius \(3a\) and total charge \(q\) is placed in \(xy-\) plane centered at origin. A point charge \(q\) is moving towards the ring along the \(z-\) axis and has speed \(v\) at \(z = 4a\). The minimum value of \(v\) such that it crosses the origin is 2019 Hard
- 190. An electric field of \(1000\,V/m\) is applied to an electric dipole at angle of \(45^o\). The value of electric dipole moment is \(10^{-29}\, C.m.\) What is the potential energy of the electric dipole? 2019 Medium
- 191. Figure shows charge \((q)\) versus voltage \((V)\) graph for series and parallel combination of to given capacitors. The capacitances are
2019 Hard - 192. For equal point charges \(Q\) each are placed in the \(xy\) plane at \((0, 2), (4, 2), (4, -2)\) and \((0, -2)\). The work required to put a fifth change \(Q\) at the origin of the coordinate system will be 2019 Hard
- 193. In free space, a particle \(A\) of charge \(1\,\mu C\) is held fixed at a point \(P.\) Another particle \(B\) of the same charge and mass \(4\,\mu g\) is kept at a distance of \(1\,mm\) from \(P\). If \(B\) is released, then its velocity at a distance of \(9\,mm\) from \(P\) is [ Take \(\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {10^9}\,N{m^2}{C^{ - 2}}\) ] 2019 Hard
- 194. In the circuit shown, find \(C\) if the effective capacitance of the whole circuit is to be \(0.5\,\mu F.\) All values in the circuit are in \(\mu F.\)
2019 Hard - 195. In the figure shown, after the switch \(‘S’\) is turned from position \(‘A’\) to position \(‘B’\), the energy dissipated in the circuit in terms of capacitance \(‘C’\) and total charge \(‘Q’\) is
2019 Hard - 196. In the figure shown below, the charge on the left plate of the \(10\, \mu F\) capacitor is \(-30\,\mu C.\) The charge on the right place of the \(6\,\mu F\) capacitor is.....\(\mu C\)
2019 Hard - 197. In the given circuit, the charge on \(4\, \mu F\) capacitor will be.....\(\mu C\)
2019 Hard - 198. The election field in a region is given by \(\vec E = (Ax + B)\hat i\) where \(E\) is in \(N\,C^{-1}\) and \(x\) in meters. The values of constants are \(A = 20\, SI\, unit\) and \(B = 10\, SI\, unit\). If the potential at \(x =1\) is \(V_1\) and that at \(x = -5\) is \(V_2\) then \(V_1 -V_2\) is.....\(V\) 2019 Medium
- 199. The give graph shown variation (with distance \(r\) from centre) of
2019 Hard - 200. The parallel combination of two air filled parallel plate capacitors of capacitance \(C\) and \(nC\) is connected to a battery of voltage, \(V\). When the capacitor are fully charged, the battery is removed and after that a dielectric material of dielectric constant \(K\) is placed between the two plates of the first capacitor. The new potential difference of the combined system is 2019 Hard
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