Advertisements
Advertisements
Question
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.
Advertisements
Solution
- The arrangement can be supposed to be a parallel combination of two capacitors each with plate area A/2 and separation. d. Total capacitance `"C"_"p" = "C"_"air" + "C"_"dielectric"`
`= (epsilon_0("A"//2))/"d" + (epsilon_0("A"//2)epsilon"r")/"d"`
`"C"_"p" = (epsilon_0"A")/"2d" (1 + epsilon_"r")` - The arrangement can be supposed to be a series combination of two capacitors, each with plate area A and separation d/2.
Total capacitance CQ = `("C"_1"C"_2)/("C"_1 + "C"_2)`
`= ((2epsilon_0"A")/"d" xx (2epsilon_"r"epsilon_0"A")/"d")/((2epsilon_0"A")/"d" + (2epsilon_"r"epsilon_0"A")/"d")`
`= (4epsilon_"r" ((epsilon_0"A")/"d")^2)/((2epsilon_0"A")/"d" (1 + epsilon_"r"))`
`= (2epsilon_"r" (epsilon_0"A")/"d")/(1 + epsilon_"r")`
`"C"_"Q" = (2epsilon_0"A")/"d" (epsilon_"r"/(1 + epsilon_"r"))`
APPEARS IN
RELATED QUESTIONS
Three identical capacitors C1, C2 and C3 of capacitance 6 μF each are connected to a 12 V battery as shown.
Find
(i) charge on each capacitor
(ii) equivalent capacitance of the network
(iii) energy stored in the network of capacitors
As `C = (1/V) Q` , can you say that the capacitance C is proportional to the charge Q?
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.
The outer cylinders of two cylindrical capacitors of capacitance 2⋅2 µF each, are kept in contact and the inner cylinders are connected through a wire. A battery of emf 10 V is connected as shown in figure . Find the total charge supplied by the battery to the inner cylinders.
Obtain the expression for capacitance for a parallel plate capacitor.
A capacitor of 4 µ F is connected as shown in the circuit (Figure). The internal resistance of the battery is 0.5 Ω. The amount of charge on the capacitor plates will be ______.
Read the following paragraph and answer the questions.
| A capacitor is a system of two conductors separated by an insulator. The two conductors have equal and opposite charges with a potential difference between them. The capacitance of a capacitor depends on the geometrical configuration (shape, size and separation) of the system and also on the nature of the insulator separating the two conductors. They are used to store charges. Like resistors, capacitors can be arranged in series or parallel or a combination of both to obtain the desired value of capacitance. |
- Find the equivalent capacitance between points A and B in the given diagram.
- A dielectric slab is inserted between the plates of the parallel plate capacitor. The electric field between the plates decreases. Explain.
- A capacitor A of capacitance C, having charge Q is connected across another uncharged capacitor B of capacitance 2C. Find an expression for (a) the potential difference across the combination and (b) the charge lost by capacitor A.
OR
Two slabs of dielectric constants 2K and K fill the space between the plates of a parallel plate capacitor of plate area A and plate separation d as shown in the figure. Find an expression for the capacitance of the system.
If the plates of a parallel plate capacitor connected to a battery are moved close to each other, then:
- the charge stored in it. increases.
- the energy stored in it, decreases.
- its capacitance increases.
- the ratio of charge to its potential remains the same.
- the product of charge and voltage increases.
Choose the most appropriate answer from the options given below:
Eight drops of mercury of equal radius and possessing equal charge combine to form a big drop. The capacitance of bigger drop as compared to each small drop is ______.
