Capacitance PYQs Set 5 (PDF)

Set 5 of 11 · Questions 121-150 of 304

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Mere Teacher · Previous Year Questions JEE Main Physics · Capacitance · Set 5 (Q121-150)
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121. $Four identical metal plates are located in air at equal distance d from each other. The area of each plate is S. If the outer most plates are connected by a conducting wire as shown in the figure the capacitance between points A and B will be$ (1) $\frac{ϵ _{0} S}{d}$ (2) $\frac{3}{2} \frac{ϵ _{0} S}{d}$ (3) $\frac{1}{2} \frac{ϵ _{0} S}{d}$ (4) $\frac{2}{3} \frac{ϵ _{0} S}{d}$ 122. $A parallel plate capacitor with plate area 'A' and distance of separation 'd' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as: ϵ (x) = ϵ_{0} + kx, for (0 < x \leq \frac{d}{2}) ϵ (x) = ϵ_{0} + k (d - x), for (\frac{d}{2} \leq x \leq d)$ (1) $(ϵ_{0} + \frac{kd}{2})^{2/ kA}$ (2) $\frac{kA}{2 ln ( \frac{2 ϵ _{0} + kd}{2 ϵ _{0}} )}$ (3) $0$ (4) $\frac{kA}{2} ln (\frac{2 ϵ _{0}}{2 ϵ _{0} - kd})$ 123. $A capacitor C_{1} = 4 μF is connected in series with another capacitor C_{2} = 1 μF . The combination is connected across d.c. source of 200 V . The ratio of potential across C_{2} to C_{1} is$ (1) $2 : 1$ (2) $4 : 1$ (3) $8 : 1$ (4) $16 : 1$ 124. $A parallel plate capacitor with air as the dielectric has capacitance C. A slab of dielectric constant K and having the same thickness as the separation between the plates is introduced so as to fill one-fourth of the capacitor as shown in the figure. The new capacitance will be$ (1) $(K + 3) \frac{C}{4}$ (2) $(K + 2) \frac{C}{4}$ (3) $(K + 1) \frac{C}{4}$ (4) $\frac{KC}{4}$ 125. $A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system [NEET 2017]$ (1) $increases by a factor of 4$ (2) $decreases by a factor of 2$ (3) $remains the same$ (4) $increases by a factor of 2$ 126. $A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at distance L from the end A is:$ (1) $\frac{Q}{8 π \in _{0} L}$ (2) $\frac{3 Q}{4 π \in _{0} L}$ (3) $\frac{Q}{4 π \in _{0} L ln 2}$ (4) $\frac{Q ln 2}{4 π \in _{0} L}$ 127. $Two identical capacitors C_{1} and C_{2} of equal capacitance are connected as shown in the circuit. Terminals a and b of the key k are connected to charge capacitor C_{1} using battery of emf V volt. Now disconnecting a and b the terminals b and c are connected. Due to this, what will be the percentage loss of energy?$ (1) $75%$ (2) $0%$ (3) $50%$ (4) $25%$ 128. $When three capacitors of equal capacities are connected in parallel and one of the same capacity is connected in series with its combination. The resultant capacity is 3.75 μF . The capacity of each capacitor is$ (1) $5 μF$ (2) $6 μF$ (3) $7 μF$ (4) $8 μF$ 129. $In the given circuit, the charge on 4 μF capacitor will be:$ (1) $5.4 μC$ (2) $9.6 μC$ (3) $13.4 μC$ (4) $24 μC$ 130. $Two capacitors of capacities 2C and C are joined in parallel and charged up to potential V. The battery is removed and the capacitor of capacity C is filled completely with a medium of dielectric constant K. The potential difference across the capacitors will now be:$ (1) $\frac{V}{K + 2}$ (2) $\frac{V}{K}$ (3) $\frac{3 V}{K + 2}$ (4) $\frac{3 V}{K}$ 131. $All capacitors used in the diagram are identical and each is of capacitance X. Then the effective capacitance between the points A and B is$ (1) $1.5 C$ (2) $6C$ (3) $C$ (4) $3C$ 132. $Calculate the amount of charge on capacitor of 4 μF . The internal resistance of battery is 1Ω :$ (1) $8 μC$ (2) $zero$ (3) $16 μC$ (4) $4 μC$ 133. $A parallel - plate capacitor with plate area A has separation between the plates. Two dielectric slabs of dielectric constant K_{1} and K_{2} of same area A/2 and thickness d/2 are inserted in the space between the plates. The capacitance of the capacitor will be given by:$ (1) $\frac{ϵ _{0} A}{d} (\frac{1}{2} + \frac{K _{1} K _{2}}{K _{1} + K _{2}})$ (2) $\frac{ϵ _{0} A}{d} (\frac{1}{2} + \frac{K _{1} K _{2}}{2 ( K _{1} + K _{2} )})$ (3) $\frac{ϵ _{0} A}{d} (\frac{1}{2} + \frac{K _{1} + K _{2}}{K _{1} K _{2}})$ (4) $\frac{ϵ _{0} A}{d} (\frac{1}{2} + \frac{2 ( K _{1} + K _{2} )}{K _{1} K _{2}})$ 134. $A capacitor of capacitance C = 1 μF is suddenly connected to a battery of 100 volt through a resistance R = 100Ω . The time taken for the capacitor to be charged to get is 50V: [Take ln 2 = 0.69]$ (1) $1.44 \times 1 0^{- 4} s$ (2) $3.33 \times 1 0^{- 4} s$ (3) $0.69 \times 1 0^{- 4} s$ (4) $0.30 \times 1 0^{- 4} s$ 135. $Find the equivalent capacitance between point A and B.$ (1) $4C$ (2) $3C$ (3) $2C$ (4) $1C$ 136. $In the circuit shown, charge on the 5 μF capacitor is$ (1) $16.36 μC$ (2) $18.00 μC$ (3) $5.45 μC$ (4) $10.90 μC$ 137. $The total charge on the system of capacitance C_{1} = 1µ F_{,} C_{2} =2µF, C_{3} =4µF and C_{4} =3µF connected in parallel is (Assume a battery of 20V is connected to the combination)$ (1) $200µC$ (2) $200C$ (3) $10µC$ (4) $10C$ 138. $A point charge +Q is placed just outside an imaginary hemispherical surface of radius R as shown in the figure. Which of the following statements is/are correct?$ (1) $Total flux through the curved and the flat surface is \frac{Q}{ϵ _{0}}$ (2) $The component of the electric field normal to the flat surface is constant over the surface$ (3) $The circumference of the flat surface is an equipotential$ (4) $The electric flux passing through the curved surface of the hemisphere is - \frac{Q}{2 ϵ _{0}} (1 - \frac{1}{2})$ 139. $A capacitor is charged by a battery. The battery is removed, and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system$ (1) $decreases by a factor of 2$ (2) $remains the same$ (3) $increases by a factor of 2$ (4) $increases by a factor of 4$ 140. $The figure shows an experimental plot discharging of a capacitor in an RC circuit. The time constant τ of this circuit lies between:$ (1) $150 sec and 200 sec$ (2) $0 and 50 sec$ (3) $50 sec and 100 sec$ (4) $100 sec and 150 sec$ 141. $A parallel plate capacitor with air medium between the plates has a capacitance of 10 μF . The area of capacitor is divided into two equal halves and filled with two media (as shown in figure) having dielectric constant K_{1} = 2 and K_{2} = 4 . The capacitance of the system will be$ (1) $10 μF$ (2) $20 μF$ (3) $30 μF$ (4) $40 μF$ 142. $The distance between two plates of a capacitor is d and its capacitance is C_{1}, when air is the medium between the plates. If a metal sheet of thickness \frac{2 d}{3} and of the same area as plate is introduced between the plates, the capacitance of the capacitor becomes C_{2} . The ratio \frac{C _{2}}{C _{1}} is$ (1) $3 : 1$ (2) $2 : 1$ (3) $4 : 1$ (4) $1 : 1$ 143. $Two non-conducting solid spheres of radii R and 2R, having uniform volume charge densities ρ_{1} and ρ_{2} respectively, touch each other. The net electric field at a distance 2R from the center of the smaller sphere, along the line joining the centers of the spheres, is zero. The ratio \frac{ρ _{1}}{ρ _{2}} can be$ (1) $-4$ (2) $- \frac{32}{25}$ (3) $\frac{32}{25}$ (4) $4$ 144. $A capacitor of capacitance 900µF is charged by a 100 V battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged capacitor. The loss of energy in this process is measured as x \times 1 0^{- 2} J. The value of x is$ 145. $A capacitor has capacitance 5µF when it's parallel plates are separated by air medium of thickness d. A slab of material of dielectric constant 1.5 having d area equal to that of plates but thickness \frac{d}{2} is inserted between the plates. Capacitance of the capacitor in the presence of slab will be_____µF.$ 146. $A composite parallel plate capacitor is made up of two different dielectric materials with different thickness (t_{1} and t_{2}) as shown in figure. The two different dielectric material are separated by a conducting foil F. The voltage of the conducting foil is____V$ 147. $An infinitely long uniform line charge distribution of charge per unit length λ lies parallel to the y-axis in the y-z plane at z = \frac{3}{2} a (see figure). If the magnitude of the flux of the electric field through the rectangular surface ABCD lying in the x-y plane with its centre at the origin is \frac{λL}{n ϵ _{0}} (ε_{0} = permittivity of free space), then the value of n is :$ 148. $A capacitor C_{1} of capacitance 5 μF is charged to a potential of 30 V using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor C2 of capacitance 10µF as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor C2 is________µC.$ 149. $A paralle plate capacitor is made up of stair like structure with a palte area A of each stair and that is connected with a wire of length b, as shown in the figure. The capacitance of the arrangement is \frac{x}{15} \frac{ϵ _{0} A}{b} . The value of x is _______.$ 150. $As show in the figure, in steady state, the charge stored in the capacitor is.......x 1 0^{- 6} C.$