Question 1 :
A parallel plate condenser with a dielectric of dielectric constant $K$ between the plates has a capacity $C$ and is charged to a potential $V$ volt. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is :<br>
Question 2 :
A parallel plate capacitor is connected to a battery. The quantities charge, voltage, electric field and energy associated with this capacitor are given by $Q_0, V_0, E_0$, and $U_0$ respectively. A dielectric slab is now introduced to fill the space between the plates with the battery still in connection. The corresponding quantities now given by $Q, V, E$ and $U$ are related to the previous ones are :<br/>
Question 3 :
A parallel plate capacitor has $91$ plates, all are identical and arranged with same spacing between them. If the capacitance between adjacent plates is $3\ pF$. What will be the resultant capacitance?
Question 4 :
Three point charges of charge $q, 2q$ and $8q$ can be placed on a $9\ cm$ long straight line. Any two charges can be placed on the two ends of the line and a third charge anywhere in between. Then, the potential energy of the system will be minimum when the charges are placed as follows
Question 5 :
A very thin metal sheet is inserted halfway between the parallel plates of an air-gap capacitor. The sheet is thin compared to the distance between the plates, and it does not touch either plate when fully inserted. The system had capacitance, $C$, before the plate is inserted.<br>What is the equivalent capacitance of the system after the sheet is fully inserted?
Question 6 :
Now consider two identical infinite cylinders, parallel to each other, posed at a distance $d > 2a$.Find the potential energy of the system (per unit length).
Question 9 :
A parallel-plate air capacitor of capacitance $C_0$ is connected to a cell of emf $V$ and then disconnected from it. A dielectric constant $K$, which can just fill the air gap of capacitor, is now inserted in it. Which of the following is incorrect?
Question 10 :
A capacitor is charged and battery is disconnected .Now the distance between the plates is increased slightly
Question 11 :
The potential difference between two points A and B is $10V$. Point A is at higher potential. If a negative charge, q = 2 C, is moved from point A to point B, then the potential energy of this charge will:<br/>
Question 12 :
A capacitor of capacitance ${C}_{0}$ is charged to a potential ${V}_{0}$ and then isolated. A small capacitor $C$ is then charged from ${C}_{0}$, discharged and charged again. This process is being repeated $n$ times. Due to this, the potential of the larger capacitor is decreased to $V$. The value of $C$ is :<br/>
Question 15 :
The capacitance of a capacitor is $10F$. The potential difference on it is $50V$. If the distance between its plate is halved, What will be the potential difference now?
Question 16 :
Two similar parallel plate capacitors each of capacity $C_o$ are connected in series, The combination is connected with a voltage source of $V_o$. Now separation between the plates of one capacitor is increased by a distance $d$ and the separation between the plates of another capacitor is decreased by the distance $d/2$ The distance between the plates of each capacitor was $d$ before the change in separation. Then, select the correct choice :<br/>
Question 17 :
A parallel plate capacitor of capacitance $C$ is connected to a battery and is charge to a potential difference $V$. Another capacitor of capacitor $2C$ is similarly charged to a potential difference $2V$. The charging battery is now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is:
Question 18 :
A regular hexagon of side 10 cm has a charge $5\mu C$ at each of its vertices. Calculate the potential at the centre of the hexagon.
Question 19 : <p>The surface of a planet is found to be uniformly charged. When a particle of mass $m$ and no charge is thrown at an angle from the surface of the planet, it has a parabolic trajectory as in projectile motion with horizontal range $L$. A particle of mass $m$ and charge $q$ with the same initial conditions has a range $\displaystyle \frac{L}{2}$. The range of particle of mass $m$ and charge $2q$ with the same initial conditions is :</p>
Question 20 :
Evaluate potential energy per ion for NaCl crystal. Use inter atomic spacing $2.82 \times 10^{10}\ m$.
Question 21 :
A parallel plate capacitor is charged from a cell and then isolated from it. The separation between the plates is now increased :<br/>
Question 22 :
A uniform electric field of magnitude $290 V/m$ is directed in the positive $x$ direction. A $+13.0 \mu C$ charge moves from the origin to the point $(x, y) = (20.0 cm, 50.0 cm).$ <br/><br/>What is the change in the potential energy of the charge field system?
Question 23 :
Three capacitance of capacity $10 \mu F , 5 \mu F $ are connected in parallel. The total capacity will be :
Question 24 :
Assertion: If three capacitors of capacitance $C_1 < C_2 < C_3$ are connected in parallel then their equivalent capacitance $C_{parallel} > C_{series}$
Reason: $\dfrac {1}{C_{parallel}}=\dfrac {1}{C_1}+\dfrac {1}{C_2}+\dfrac {1}{C_3}$
Question 25 :
The space between the plates of a parallel plate capacitor is filled with a 'dielectric' whose 'dielectric constant' varies with distance as per the relation, $K(x)=K_o+\lambda x(\lambda=a$ constant) The capacitance C, of this capacitor, would be related to its 'vacuum' capacitance $C_o$ as per the relation :<br/>
Question 26 :
The dielectric strength of air is $3 \times10^{6}$V /m. A parallel plate air capacitor has area $20cm$ <br> $^2$ and plate separation $1$ mm. Then maximum r.m.s. voltage of an A.C. source which can be safely connected to this capacitor is<br/>
Question 27 :
The energy of a parallel plate capacitor when connected to a battery is $E$. With the battery still in connection, if the plates of the capacitor are separated so that the distance between them is twice the original distance, then electrostatic energy becomes :<br/>
Question 28 :
A particle of mass $10^{-3}kg$ and charge $5\mu C$ is thrown at a speed $20\ m\ s^{-1}$ against a uniform electric field of strength $2\times 10^{5}N\ C^{-1}$. How much distance will it travel before coming to rest momentarily?
Question 29 :
The electric potential at a certain distance from a point charge $Q$ is $810 V$ and electric field is $300 N/C$. The minimum speed with which a particle of charge $-Q$ and mass $m = 6 \times 10^{-16} kg$ should be projected from that point so that it moves into the field free region is:
Question 30 :
Two parallel plate capacitors of capacitances $C$ and $2C$ are connected in parallel and charged to a potential difference $V$. The battery is then disconnected and the region between the plates of the capacitor $C$ is completely filled with a material of dielectric constant $K$. The potential difference across the capacitors now becomes :<br/>
Question 31 :
$15$ joule of work has to be done to take a charge of $0.01 C $ from $A$ to $B$ . The potential difference $(V_B - V_A)$ is
Question 32 :
At the moment $t=0$, an electron leaves one plate of a parallel-plate condenser with a negligible velocity. An accelerating voltage varying as $V=at$, where $a$ is a constant is applied between the plates. The separation between the plates is $l$. The velocity of the electron at the moment it reaches the opposite plate will be :<br/>
Question 33 :
How much work would be required to move a proton from the negative to the positive plate?
Question 34 :
Electric potential due to a point charge $q$ at a distance $r$ from is given by
Question 35 :
A parallel plate air capacitor has a initial capacitance $C$. If plate separation is slowly increased from ${d}_{1}$ to ${d}_{2}$, then mark the correct statement(s). (Take potential of the capacitor to be constant, i.e., throughout the process it remains connected to battery.)<br>
Question 36 :
Two condensers of capacity $0.3 \mu F$ and $0.6 \mu F$ respectively are connected in series. The combination is connected across a potential of $6$ volts. The ratio of energies stored by the condensers will be:
Question 37 :
A parallel plate capacitor of plate area $A$ and plate separation $d$ is charged to potential difference $V$ and then the battery is disconnected. A slab of dielectric constant $K$ is then inserted between the plates of capacitor so as to fill the space between the plates. If $Q, E$ and $W$ denote respectively, the magnitude of charge on each plate electric field between the plates (after the slab is inserted), and work done on the system, in question, in the process of inserting the slab, then which is wrong?<br/>
Question 38 :
The energy required to charge a parallel plate condenser of plate separation d and plate area of cross-section A such that the uniform electric field between the plates is E, is :<br/>
Question 39 :
A parallel plate capacitor is charged and then disconnected from the charging battery. If the plates are now moved farther apart by pulling at them by means of insulating handles, then:
Question 40 :
The potential in certain region is given as $V = 2x^2$, then the charge density of that region is
Question 42 :
A parallel plate capacitor has a capacity $80\times 10^{-6}\ F$ when air is present between the plates. The volume between the plates is then completely filled with a dielectric slab of dielectric constant $20$. The capacitor is now connected to a battery of $30\ V$ by wires. The dielectric slab is then removed. Then, the charge that passes now through the wire is :
Question 44 :
Assertion: STATEMENT-1 : To put a dielectric plate in the inter space between two plates of a capacitor connected to a D.C. voltage external agency has to do negative work.
Reason: STATEMENT-2 : Putting the dielectric increases the capacitance.
Question 45 :
Two fixed charges $- 2Q$ and $+Q$ are located at points $(- 3a, 0)$ and $(+ 3a, 0)$ respectively, Then which of the following statement is correct?
Question 46 :
The following operation can be performed on a capacitor:<br>X connect the capacitor to a battery of emf E.<br>Y disconnect the battery.<br>Z reconnect the battery with the polarity reversed.<br>W insert a dielectric slab in the capacitor.
Question 47 : Match the following two columns:<br><table class="wysiwyg-table"><tbody><tr><td></td><td>Column I</td><td></td><td>Column II</td></tr><tr><td>A.</td><td>Electrical resistance</td><td>$1.$</td><td>$[ML^{3}T^{-3}A^{-2}]$</td></tr><tr><td>B.</td><td>Electrical potential</td><td>$2.$</td><td>$[ML^{2}T^{-3}A^{-2}]$</td></tr><tr><td>C.</td><td>Specific resistance</td><td>$3.$</td><td>$[ML^{2}T^{-3}A^{-1}]$</td></tr><tr><td>D.</td><td>Specific conductance</td><td>$4.$</td><td>None of these</td></tr></tbody></table>
Question 48 :
Two points P and Q are maintained at potentials of of $10V$ and $-4V$ respectively. The work done in moving $100$ electrons from P to Q is proportional to
Question 49 :
Two charges $5\times 10^{-8}C$ and $-3\times 10^{-8}C$ are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
Question 50 :
A series combination of $n_1$ capacitors, each of value $C_1$, is charged by a source of potential difference 4 V. When another parallel combination of $n_2$ capacitors, each of value $C_2$, is charged by a source of potential difference V, it has the same (total) energy stored in it, as the first combination has. The value of $C_2$, in terms of $C_1$, is then<br>
