More about Q=CV

Q. two charges -4q and q are kept at (-a, 0) and (a, 0) respectively. The graph showing in the variation of electric field along x axis is

Q. Three charges each of magnitude q are placed at vertices of an equilateral triangle. A fourth charge -Q is placed at centroid of triangle so that system of 4 charges remains in equilibrium. Magnitude of charge Q is such that q = nQ, where n is (Answer upto two decimal places)

Q.

Obtain the formula for the electric field due to a long thin wire of uniform linear charge density λ without using Gauss’s law. [Hint: Use Coulomb’s law directly and evaluate the necessary integral.]

Q. 104.In the circuit shown in the figure, if potential at point A is taken to be zero, the potential at point B is ?

Q. The potentials of the two plates of capacitor are + 10V and -10 V. The charge on one of the plates is 40 C. The capacitance of the capacitor is
[AFMC 2005]

1. 2 F
2. 0.5 F
3. 0.25 F
4. 4 F

Q. For the circuit arrangement shown in figure, the charge on the capacitor in the steady state condition is

1. $14\mu C$
2. $18\mu C$
3. $20\mu C$
4. $12\mu C$

Q. 221. A plastic rod of length 1.0 m carries uniform positive charge +4.0 HC/m on half of its length and uniform negative charge 4.0 C/m on the remaining half of its length. Find magnitude of its net dipole moment. of (1) 1 HCm (3) 4 Cm (2) 2 uCm (4) 8 HCm

Q. Two condensers C₁ and C₂ in a circuit are joined as shown in the figure The potential of point A is V₁ and that of B is V₂. The potential of point D will be

1. 
   

2. 
   

3. 
   

4. 
   

Q.

A capacitor stores charge Q at a potential difference V. If the voltage applied by a battery to the capacitor is doubled to 2V, then

1. The capacitance and the charge both fall to half their initial values

2. The capacitance falls to half its initial value and the charge remains the same

3. The capacitance remains the same and the charge doubles

4. The capacitance and the charge both double

Q. A positively charged body $\text{A}$ has been brought near a neutral brass sphere $\text{B}$ mounted on a glass stand as shown in the figure. The potential of $\text{B}$ will be-

1. Zero
2. Negative
3. Positive
4. Infinite

Q. In the situation shown in the figure, we have three concentric metallic shells. The inner and outer shells are earthed, but the middle shell is given charge $+Q$. Comment on the electric field in the different regions.

1. Electric field in region III is zero.
2. Electric field in region II is outwards.
3. Electric field in region I is zero.
4. Electric field in region I is inwards.

Q. Consider two concentric conducting spheres. The outer sphere is hollow and the inner sphere is solid. Initially, they are given a charge $-7Q$ and a charge $-2Q$ respectively, then the charges on the outer surface and inner surface of the outer sphere is

1. $-2Q,-7Q$
2. $+2Q,-9Q$
3. $-2Q,-5Q$
4. $+2Q,+5Q$

Q.

Two charged spheres of radii $10cm$ and $15cm$ are connected by a thin wire. If no current flows through the wire, then they have

1. same material density
2. the same potential
3. the same field on their surfaces
4. diffferent potential

Q. The current through the $5\Omega$ resistor is

1. $10\text{A}$
2. $1\text{A}$
3. $2.5\text{A}$
4. $0.4\text{A}$

Q. Among two spheres A and B first radius 10 cm and charge 10^-6C and second has the radius 30 cm and charge 10^-5 when they are touched charge on both are Q_{​​​​​​a ​​​​​​} and Qb respectively

Q.

A charge of $+2.0\times {10}^{-8}C$ is placed on the positive plate and a charge of $-1.0\times {10}^{-8}C$ on the negative plate of a parallel-plate capacitor of capacitance $1.2\times {10}^{-3}\mu F.$

Calculate the potential difference developed between the plates.

Q.

Two insulated charged spheres of radii 20cm and 25cmrespectively and

having an equal charge Q are connected by a copper wire, then they are

separated

1. Charge on each of the sphere will be 2Q

2. Both the spheres will have the same charge Q

3. Charge on the 20cm sphere will be greater than that on the 25cm sphere

4. Charge on the 25cm sphere will be greater than that on the 20cm sphere

Q. Two charges 10 uC and -10 HC are placed at points A and B separated by a distance of 10cm .Find the field at a point P on the perpendicular bisector of AB at a distance of 12 cm from its middle poi

Q. A parallel plate capacitor is made of two circular plates separated by an distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is $3\times {10}^{4}V/m$, the charge density of the positive plate will be close to:

1. $3\times {10}^{4}C/m^2$
2. $3\times {10}^{-7}C/m^2$
3. $6\times {10}^{4}C/m^2$
4. $6\times {10}^{-7}C/m^2$

Q. The radii of the inner and outer spheres of a condenser are 9 cm and 10 cm respectively. If the dielectric constant of the medium between the two spheres is 6 and charge on the inner sphere is $18\times {10}^{-9}$ coulomb , then the potential of inner sphere will be, if the outer sphere is earthed

1. 90 volts
2. 180 volts
3. 30 volts
4. 18 volts

Q. A potentiometer wire has length 4m and resis†an ce 8 ohm the resis†an ce that must be connected in series with the wire and an accumulator oh emf 2v so as to get a potential gradient 1mV per cm on the wire i

Q.

In the series LCR circuit at resonance the applied ac voltage is 220V. The potential drop across the inductance is 110 V. what is the potential drop across the resistance?

1. 220 V

2. 

3. 

4. 110 V

Q. A capacitor of capacity $C_1$, is charged by connecting it across a battery of emf $V_o$. The battery is then removed and the capacitor is connected in parallel with an uncharged capacitor of capacity $C_2$. The potential difference across this combination is

1. $\frac{C_2}{C_1+C_2}{V}_o$
   
2. $\frac{C_1}{C_1+C_2}{V}_o$
   
3. $\frac{C_1+C_2}{C_2}{V}_o$
   
   
4. $\frac{C_1+C_2}{C_1}{V}_o$
   

Q. A cylindrical capacitor of inner radii $R$ and outer radii $2R$ is filled with two dielectrics of constant $K_1$ and $K_2$ respectively. Each dielectric occupies half the length of the cylinder. Find the capacitance of the system between the inner and outer cylinders.

1. $\frac{2\pi {\epsilon }_{0}L}{\ln \left(2\right)}\left(\frac{K_1{K}_2}{K_1+K_2}\right)$
2. $\frac{\pi {\epsilon }_{0}L}{\ln R}(K_1+K_2)$
3. $\frac{\pi {\epsilon }_{0}L}{\ln \left(2\right)}(K_1+K_2)$
4. $\frac{\pi {\epsilon }_{0}L}{2\ln \left(2\right)}(K_1+K_2)$

Q.

Take the potential of the point B in figure (31-E7) to be zero. (a) Find the potentials at the points C and D. (b) If a capacitor is connected between C and D, what charge will appear on this capacitor ?

Q. Three large identical conducting parallel plates carrying charge $+Q,-Q$ and $+2Q$ respectively, are placed as shown in the figure. If $E_A,E_B$, and $E_C$ refer to the magnitudes of the electric fields at points $A,B$ and $C$ respectively, then

1. $E_A>E_B>E_C$
2. $E_A=0$ and $E_C>E_B$
3. $E_A=0$ and $E_B>E_C$
4. $E_A=0$ and $E_B=E_C$

Q.

Each of the plates shown in figure (31-E19) has surface area $\left(\frac{96}{{\in }_0}\right)\times {10}^{-12}Fm$ on one side and the separation between the consecutive plates is 4.0 mm. The emf of the battery connected is 10 volts. Find the magnitude of the charge supplied by the battery to each of the plates connected to it.

Q. A parallel plate air capacitor with no dielectric between the plates is connected to the constant voltage source. How would capacitance and charge change if the dielectric constant $K=2$ is inserted between the plates ?
$C_0$ and $Q_0$ are the capacitance and charge of the capacitor before the introduction of the dielectric.

1. $C_0/2\text{and}2Q_0$
2. $2C_0\text{and}{Q}_0/2$
3. $C_0/2\text{and}{Q}_0/2$
4. $2C_0\text{and}2Q_0$

Q. A charged conducting sphere of radius 1.3m has uniform surface charge density 50.0μ Cm^{-2}. The charge on the sphere is (1) 1.06×10^{-3 } C (2) 2.12×10^{-4} C (3) 0.50×10^{-3} C (4) 3.0×10^{-3} C

Q. 33.The potential difference in volt across the resistance R3 in the circuit shown in fig is :(values are given in the diagram ) A)5 B)7.5 C)15 D)12.5