Advertisements
Advertisements
प्रश्न
Obtain an expression for equivalent capacitance when three capacitors C1, C2 and C3 are connected in series.
उत्तर
All the capacitors are connected in series, In the fig. are shown three capacitors of capacity C1, C2, C3 connected in series. The charge Q flowing through each of the capacitors is the same but potential difference across them will be different. If V1, V2, and V3 are the potential difference across them, then
`"V"_1 = "Q"/"C"_1 , "V"_2 = "Q"/"C"_2 , "V"_3= "Q"/"C"_3`
If C is the capacitance of the combination, then
V = `"Q"/"C"`
Also, V = V1 + V2 + V3
or `"Q"/"C" = "Q"/"C"_1 + "Q"/"C"_2 + "Q"/"C"_3`
`1/"C" = 1/"C"_1 +1/"C"_2 + 1/"C"_3` , which is the required relation.
संबंधित प्रश्न
A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports. Show that the capacitance of a spherical capacitor is given by
C = `(4piin_0"r"_1"r"_2)/("r"_1 - "r"_2)`
where r1 and r2 are the radii of outer and inner spheres, respectively.
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?
Find the equivalent capacitance of the infinite ladder shown in figure between the points A and B.
Consider the situation shown in the figure. The switch S is open for a long time and then closed. (a) Find the charge flown through the battery when the switch S is closed. (b) Find the work done by the battery.(c) Find the change in energy stored in the capacitors.(d) Find the heat developed in the system.
The separation between the plates of a parallel-plate capacitor is 0⋅500 cm and its plate area is 100 cm2. A 0⋅400 cm thick metal plate is inserted into the gap with its faces parallel to the plates. Show that the capacitance of the assembly is independent of the position of the metal plate within the gap and find its value.
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.
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`
Obtain the expression for capacitance for a parallel plate capacitor.
Derive the expression for resultant capacitance, when the capacitor is connected in series.
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.
