Advertisements
Advertisements
प्रश्न
Obtain the equivalent capacitance of the network in Figure. For a 300 V supply, determine the charge and voltage across each capacitor.
Advertisements
उत्तर
Capacitance of capacitor C1 is 100 pF.
Capacitance of capacitor C2 is 200 pF.
Capacitance of capacitor C3 is 200 pF.
Capacitance of capacitor C4 is 100 pF.
Supply potential, V = 300 V
Capacitors C2 and C3 are connected in series.
Let their equivalent capacitance be C'
∴ `1/"C'" = 1/200 + 1/200 = 2/200`
∴ C' = 100 pF
Capacitors C1 and C' are in parallel. Let their equivalent capacitance be C''.
∴ `"C''" = "C'" + "C"_1`
= 100 + 100
= 200 pF
C'' and C4 are connected in series. Let their equivalent capacitance be C.
∴ `1/C = 1/("C''") + 1/("C"_4)`
= `1/200 + 1/100`
= `(2 + 1)/200`
C = `200/3` pF
Hence, the equivalent capacitance of the circuit is `200/3` pF.
Potential difference across C" = V"
Potential difference across C4 = V4
∴ `"V''" + "V"_4 = "V" = 300 "V"`
Charge on C4 is given by
Q4 = CV
= `200/3 xx 10^-12 xx 300`
= `2 xx 10^-8 "C"`
∴ `"V"_4 = "Q"_4/"C"_4`
= `(2 xx 10^-8)/(100 xx 10^-12)` = 200 V
∴ Voltage across C1 is given by
`"V"_1 = "V" - "V"_4`
= `300 - 200 = 100 "V"`
Hence, potential difference, V1, across C1 is 100 V.
Charge on C1 is given by,
`"Q"_1 = "C"_1"V"_1`
= `100 xx 10^-12 xx 100`
= `10^-8 "C"`
C2 and C3 have the same capacitances have a potential difference of 100 V together. Since C2 and C3 are in series, the potential difference across C2 and C3 is given by,
V2 = V3 = 50 V
Therefore, charge on C2 is given by,
`"Q"_2 = "C"_2"V"_2`
= `200 xx 10^-12 xx 50`
= `10^-8 "C"`
And charge on C3 is given by,
`"Q"_3 = "C"_3"V"_3`
= `200 xx 10^-12 xx 50`
= `10^-8 "C"`
Hence, the equivalent capacitance of the given circuit is `200/3` pF with
Q1 = 10−8 C, V1 = 100 V
Q2 = 10−8 C, V2 = 50 V
Q3 = 10−8 C, V3 = 50 V
Q4 = 2 × 10−8 C, V4 = 200 V
APPEARS IN
संबंधित प्रश्न
Define capacitor reactance. Write its S.I units.
(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 identical capacitors of 12 pF each are connected in series across a battery of 50 V. How much electrostatic energy is stored in the combination? If these were connected in parallel across the same battery, how much energy will be stored in the combination now?
Also find the charge drawn from the battery in each case.
Find the charge appearing on each of the three capacitors shown in figure .
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.
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.
Consider an assembly of three conducting concentric spherical shell of radii a, b and c as shown in figure Find the capacitance of the assembly between the points Aand B.
Suppose the space between the two inner shells is filled with a dielectric of dielectric constant K. Find the capacitance of the system between 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.
The figure show a network of five capacitors connected to a 10V battery. Calculate the charge acquired by the 5μF capacitor.
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?
When air is replaced by a dielectric medium of constant K, the maximum force of attraction between two charges separated by a distance ______.
The radius of a sphere of capacity 1 microfarad in the air is ______
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 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 ______.
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.
Two spherical conductors of capacities 4 µF and 3 µF are charged to same potential having radii 4 cm and 3 cm respectively. If ‘σ1’ and ‘σ2’ represent surface density of charge on respective conductors then ______.
