Advertisements
Advertisements
Question
Find the capacitances of the capacitors shown in figure . The plate area is Aand the separation between the plates is d. Different dielectric slabs in a particular part of the figure are of the same thickness and the entire gap between the plates is filled with the dielectric slabs.
Advertisements
Solution
The two parts of the capacitor are in series with capacitances C1 and C2.
Here,
`C_1 = (K_1∈_0A)/(d/2) and C_2 = (K_2∈_0A)/(d/2)`
⇒ `C_1 = (2K_1∈_0A)/d and C_2 = (2K_2∈_0A)/d`
Because they are in series, the net capacitance is calculated as :
`C = (C_1 xx C_2)/(C_1+C_2)`
= `((2K_1∈_0A)/d xx (2K_2∈_0A)/d)/((2K_1∈_0A)/d xx (2K_2∈_0A)/d)`
= `(2K_1K_2∈_0A)/(d(K_1+K_2)`
(b) Here, the capacitor has three parts. These can be taken in series.
Now ,
`C_1 = (K_1∈_0A)/((d/3)) = (3K_1∈_0A)/d`
`C_2 = (3K_2∈_0A)/d`
`C_3 = (3K_3∈_0A)/d`
Thus, the net capacitance is calculated as :
`C = (C_1 xx C_2 xx C_2)/(C_1C_2+C_2C_3+C_3C_1)`
= `((3K_1∈_0A)/d xx (3K_2∈_0A)/d xx (3K_3∈_0A)/d)/((3K_1∈_0A)/d xx (3K_2∈_0A)/d xx (3K_2∈_0A)/d xx (3K_3∈_0A)/d xx (3K_3∈_0A)/d xx (3K_1∈_0A)/d)`
= `(3 ∈_0 K_1K_2K_3)/(d(K_1K_2+K_2K_3+K_3K_1)`
(c)
Here ,
`C_1 = (K_1∈_0A/2)/d = (K_1∈_0A)/(2d)`
`C_2 = (K_2∈_0A)/(2d)`
These two parts are in parallel.
`therefore C = C_1 + C_2`
= `(∈_0A)/(2d)(K_1+K_2)`
APPEARS IN
RELATED QUESTIONS
A capacitor of capacitance ‘C’ is charged to ‘V’ volts by a battery. After some time the battery is disconnected and the distance between the plates is doubled. Now a slab of dielectric constant, 1 < k < 2, is introduced to fill the space between the plates. How will the following be affected? (a) The electric field between the plates of the capacitor Justify your answer by writing the necessary expressions.
A parallel plate capacitor of capacitance C is charged to a potential V. It is then connected to another uncharged capacitor having the same capacitance. Find out the ratio of the energy stored in the combined system to that stored initially in the single capacitor.
The plates of a parallel-plate capacitor are made of circular discs of radii 5⋅0 cm each. If the separation between the plates is 1⋅0 mm, what is the capacitance?
Each of the capacitors shown in figure has a capacitance of 2 µF. find the equivalent capacitance of the assembly between the points A and B. Suppose, a battery of emf 60 volts is connected between A and B. Find the potential difference appearing on the individual capacitors.
A capacitor of capacitance 2⋅0 µF is charged to a potential difference of 12 V. It is then connected to an uncharged capacitor of capacitance 4⋅0 µF as shown in figure . Find (a) the charge on each of the two capacitors after the connection, (b) the electrostatic energy stored in each of the two capacitors and (c) the heat produced during the charge transfer from one capacitor to the other.
A 5⋅0 µF capacitor is charged to 12 V. The positive plate of this capacitor is now connected to the negative terminal of a 12 V battery and vice versa. Calculate the heat developed in the connecting wires.
A parallel-plate capacitor of plate area A and plate separation d is charged to a potential difference V and then the battery is disconnected. A slab of dielectric constant K is then inserted between the plates of the capacitor so as to fill the space between the plates. Find the work done on the system in the process of inserting the slab.
Consider the situation shown in figure. The plates of the capacitor have plate area A and are clamped in the laboratory. The dielectric slab is released from rest with a length a inside the capacitor. Neglecting any effect of friction or gravity, show that the slab will execute periodic motion and find its time period.
Three circuits, each consisting of a switch 'S' and two capacitors, are initially charged, as shown in the figure. After the switch has been closed, in which circuit will the charge on the left-hand capacitor
(i) increase,
(ii) decrease, and
(iii) remains the same? Give reasons.
Calculate the resultant capacitances for each of the following combinations of capacitors.
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?
For the given capacitor configuration
- Find the charges on each capacitor
- potential difference across them
- energy stored in each capacitor.
Capacitors P and Q have identical cross-sectional areas A and separation d. The space between the capacitors is filled with a dielectric of dielectric constant Er as shown in the figure. Calculate the capacitance of capacitors P and Q.
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 ______.
Between the plates of parallel plate condenser there is 1 mm thick medium shoot of dielectric constant 4. It is charged at 100 volt. The electric field in volt/meter between the plates of capacitor is ______.
For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant K is used, which has the same area as the plates of the capacitor.
The thickness of the dielectric slab is `3/4`d, where 'd' is the separation between the plate of the parallel plate capacitor.
The new capacitance (C') in terms of the original capacitance (C0) is given by the following relation:
A capacitor has charge 50 µC. When the gap between the plate is filled with glass wool, then 120 µC charge flows through the battery to capacitor. The dielectric constant of glass wool is ______.
