Advertisements
Advertisements
Question
A parallel-plate capacitor has plate area 25⋅0 cm2 and a separation of 2⋅00 mm between the plates. The capacitor is connected to a battery of 12⋅0 V. (a) Find the charge on the capacitor. (b) The plate separation is decreased to 1⋅00 mm. Find the extra charge given by the battery to the positive plate.
Solution
Given :
Area of the plate , `A = 25 "cm"^2 = 25 xx 10^-4 "m"^2`
Separation between the plates, `d = 2 "mm" = 2 xx 10^-3 "m"`
Potential difference between the plates, V = 12 V
The capacitance of the given capacitor is given by
`C = (∈_0A)/d`
= `((8.85 xx 10^-12) xx (25 xx 10^-4))/((2 xx 10^-3))`
= `11.06 xx 10^-12 "F"`
(a) Charge on the capacitor is given by
Q = CV
= `11.06 xx 10^-12 xx 12`
= `1.33 xx 10^-10 "C"`
(b) When the separation between the plates is decreased to 1 mm , the capacitance `C^'` can be calculated as :
`C^' = (∈_0A)/d`
= `((8.85 xx 10^-12) xx (25 xx 10^-4))/(1 xx 10^-3)`
= `22.12 xx 10^-12 "F"`
Charge on the capacitor is given by
`Q^' = C^'V`
= `22.12 xx 10^-12 xx 12`
= `2.65 xx 10^-10 "C"`
Extra Charge
= `(2.65 xx 10^-10 - 1.32 xx 10^-10) C`
= `1.33 xx 10^-10 "C"`
APPEARS IN
RELATED QUESTIONS
A capacitor of capacitance C is charged fully by connecting it to a battery of emf E. It is then disconnected from the battery. If the separation between the plates of the capacitor is now doubled, how will the following change?
(i) charge stored by the capacitor.
(ii) Field strength between the plates.
(iii) Energy stored by the capacitor.
Justify your answer in each case.
Obtain the equivalent capacitance of the network in Figure. For a 300 V supply, determine the charge and voltage across each capacitor.
(i) Find equivalent capacitance between A and B in the combination given below. Each capacitor is of 2 µF capacitance.
(ii) If a dc source of 7 V is connected across AB, how much charge is drawn from the source and what is the energy stored in the network?
Two conducting spheres of radii R1 and R2 are kept widely separated from each other. What are their individual capacitances? If the spheres are connected by a metal wire, what will be the capacitance of the combination? Think in terms of series−parallel connections.
Find the equivalent capacitance of the infinite ladder shown in figure between the points A and B.
An air-filled parallel-plate capacitor is to be constructed which can store 12 µC of charge when operated at 1200 V. What can be the minimum plate area of the capacitor? The dielectric strength of air is `3 xx 10^6 "Vm"^-1`
Figure shows two parallel plate capacitors with fixed plates and connected to two batteries. The separation between the plates is the same for the two capacitors. The plates are rectangular in shape with width b and lengths l1 and l2. The left half of the dielectric slab has a dielectric constant K1 and the right half K2. Neglecting any friction, find the ration of the emf of the left battery to that of the right battery for which the dielectric slab may remain in equilibrium.
Obtain the expression for energy stored in the parallel plate capacitor.
Derive the expression for resultant capacitance, when the capacitor is connected in parallel.
During a thunder storm, the movement of water molecules within the clouds creates friction, partially causing the bottom part of the clouds to become negatively charged. This implies that the bottom of the cloud and the ground act as a parallel plate capacitor. If the electric field between the cloud and ground exceeds the dielectric breakdown of the air (3 × 106 Vm–1), lightning will occur.
- If the bottom part of the cloud is 1000 m above the ground, determine the electric potential difference that exists between the cloud and ground.
- In a typical lightning phenomenon, around 25 C of electrons are transferred from cloud to ground. How much electrostatic potential energy is transferred to the ground?
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 ______.
The positive terminal of 12 V battery is connected to the ground. Then the negative terminal will be at ______.
The work done in placing a charge of 8 × 10–18 coulomb on a condenser of capacity 100 micro-farad is ______.
Two spherical conductors A and B of radii a and b(b > a) are placed concentrically in the air. B is given a charge +Q and A is earthed. The equivalent capacitance of the system is ______.
The radius of a sphere of capacity 1 microfarad in the air is ______
Consider two conducting spheres of radii R1 and R2 with R1 > R2. If the two are at the same potential, the larger sphere has more charge than the smaller sphere. State whether the charge density of the smaller sphere is more or less than that of the larger one.
Can the potential function have a maximum or minimum in free space?
A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (U) as ε = αU where α = 2V–1. A similar capacitor with no dielectric is charged to U0 = 78V. It is then connected to the uncharged capacitor with the dielectric. Find the final voltage on the capacitors.
A capacitor of capacity 2 µF is charged to a potential difference of 12 V. It is then connected across an inductor of inductance 0.6 mH. The current in the circuit at a time when the potential difference across the capacitor is 6.0 V is ______ × 10-1A.
