Capacitance of Parallel Plate Capacitor

Q.

A simple pendulum of period T has a metal bob which is negatively charged. If it is allowed to oscillate above a large positively charged metallic plate, its period of oscillation will be,

1. Increases

2. Remains the same

3. May increase or decrease

4. Decreases

Q. If an electron enters into a space between the plates of a parallel plate capacitor at an angle $\alpha$ with the plates and leaves at an angle $\beta$ to the plates. The ratio of its kinetic energy while entering the capacitor to that while leaving will be

1. ${\left(\frac{\cos \alpha }{\cos \beta }\right)}^2$
2. ${\left(\frac{\cos \beta }{\cos \alpha }\right)}^2$
3. ${\left(\frac{\sin \alpha }{\sin \beta }\right)}^2$
4. ${\left(\frac{\sin \beta }{\sin \alpha }\right)}^2$

Q. A toroid having inner radius 10cm, outer radius 11cm and 10000 turns is carrying current 2A. Magnetic field at a point at distance 5cm from the centre of its curvature is

Q.

Where is the electric field uniform?

Q. 86. In Seebeck effect , why the potential drop between two junctions and thermoelectric EMF are said to be same.

Q. A parallel plate capacitor has a uniform electric field $E$ in the space between the plates. If the distance between the plates is $d$ and area of each plate is $A$, the energy stored in the capacitor is

1. $\frac{1}{2}{\epsilon }_0{E}^{2}Ad$
2. ${\epsilon }_{0}AEd$
3. $\frac{E^{2}Ad}{{\epsilon }_0}$
4. $\frac{1}{2}{\epsilon }_0{E}^2$

Q.

Two parallel plate capacitors of capcitances C and 2C are connected in parallel and changed to a potential V by a battery. The battery is then disconnected and the apsce between the plates of capacitor C is completely filled with a material of dielectric constant K. The potential difference across the capacitors now becomes

1. $\frac{V}{K+1}$
   

2. $\frac{2V}{K+2}$
   

3. $\frac{3V}{K+2}$
   

4. $\frac{3V}{K+3}$

Q.

What is the dimensional formula of capacity?

Q.

The introduction of a metal plate between the plates of a parallel plate capacitor increases its capacitance by 4.5 times. If d is the separation of the two plates of the capacitor, the thickness of the metal plate introduced is

1. $\frac{d}{3}$
   

2. $\frac{5d}{9}$
   

3. $\frac{7d}{9}$
   

4. d

Q. Two square plates of side 1 m are placed at a separation of 1 mm in vacuum to form a parallel plate capacitor. Its capacitance is?

1. 9nF
2. 90nF
3. 900nF
4. 0.9 nF

Q. Prove that kinetic energy = $1/2I_P{\omega }^2$

Q. I have two parallel charged plates at a distance 10cm from each other with air in between. What should be the minimum potential difference between the plates to get charges flowing between them?
(Dielectric strength of air : $3\times {10}^{6}V{m}^{-1})$

1. 1000V
2. 2000V
3. 3000V
4. None of these

Q. In the given circuit if each plate surface area is $A$ and plate seperation is $d$. Choose the correct option(s).

1. Equivalent capacitance of system is $\frac{2{ϵ}_{o}A}{d}$
2. Energy stored between plates $1$ and $2$ is $\frac{{ϵ}_{o}A{\text{E}}^2}{2d}$
3. Energy stored between plates $3$ and $4$ is zero
4. Equivalent capacitance of system is $\frac{5{ϵ}_{o}A}{4d}$