Advertisements
Advertisements
प्रश्न
A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = 10−12 F). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?
Advertisements
उत्तर
Capacitance between the parallel plates of the capacitor, C = 8 pF
Initially, the distance between the parallel plates was d and it was filled with air. The dielectric constant of air, k = 1
Capacitance, C, is given by the formula,
`"C" = ("k"in_0"A")/"d"`
= `(in_0"A")/"d"` .......(i)
Where,
A = Area of each plate
`in_0` = Permittivity of free space
If the distance between the plates is reduced to half, then the new distance, d’ = `"d"/2`
Dielectric constant of the substance filled in between the plates, k' = 6
Hence, the capacitance of the capacitor becomes
`"C'" = ("k'"in_0"A")/"d"`
= `(6in_0"A")/("d"/2)` ........(ii)
Taking ratios of equations (i) and (ii), we obtain
C' = 2 × 6 C
= 12 C
= 12 × 8
= 96 pF
Therefore, the capacitance between the plates is 96 pF.
APPEARS IN
संबंधित प्रश्न
Derive the expression for the capacitance of a parallel plate capacitor having plate area A and plate separation d.
What meaning would you give to the capacitance of a single conductor?
Four capacitors, C1, C2, C3 andC4 are connected as shown in Figure 3 below. Calculate equivalent capacitance of the circuit between points X . and Y.
A capacitor, made of two parallel plates each of plate area A and separation d, is being charged by an external ac source. Show that the displacement current inside the capacitor is the same as the current charging the capacitor.
Net capacitance of three identical capacitors in series is 2 μF. What will be their net capacitance if connected in parallel?
The dielectric constant decreases if the temperature is increased. Explain this in terms of polarization of the material.
When a dielectric slab is gradually inserted between the plates of an isolated parallel-plate capacitor, the energy of the system decreases. What can you conclude about the force on the slab exerted by the electric field?
Define the dielectric constant of a medium. What is its S.I unit?
Two parallel uniformly charged infinite plane sheets, '1' and '2', have charge densities + `sigma and -2sigma `respectively. Give the magnitude and direction of the net electric field at a point.
(i) in between the two sheets and
(ii) outside near the sheet '1'.
Two metal plates are separated by 2 cm. The potentials of the plates are -10 V and + 30 V. The electric field between the two plates is ______.
A dielectric is inserted between the plates of a charged and isolated parallel-plate air capacitor. Then, the charge on the plates and the potential difference, respectively, ______.
Capacity of a parallel plate capacitor with a medium of dielectric constant 8 is 12 µF. If the medium is removed, then capacity of the capacitor would be ____________.
Four capacitors of equal capacity have an equivalent capacitance C1 when connected in series and an equivalent capacitance C2 when connected in parallel. The ratio `c_2/c_1`, is ______
A free electron and a free proton are placed between two oppositely charged parallel plates. Both are closer to the positive plate than the negative plate.
Which of the following statements is true?
- The force on the proton is greater than the force on the electron.
- The potential energy of the proton is greater than that of the electron.
- The potential energy of the proton and the electron is the same.
The energy required to charge a parallel plate condenser of plate separation d and plate area of cross-section A such that the uniform electric field between the plates is E is:
The separation between the plates of the parallel plate capacitor is d and the area of each plate is A. When a slab of material of dielectric constant k and thickness t(t < d) is introduced between the plates, its capacitance becomes ______.
(ε0 = permittivity of free space)
A dielectric slab of dielectric constant K and thickness t is introduced between the two plates of a capacitor of plate-separation d (>t) and common area A. The capacitance of this system is given as:
`C = (∈_o"A")/((d-t)+(t/k))`
How does the capacitance C modify in each of the following cases?
- The dielectric slab covers half the distance of separation between the two plates.
- The whole space between the plates is filled with the dielectric.
The capacity of a parallel plate air capacitor is \[C_0\] and the distance of separation of the plates is d. A dielectric slab of thickness \[\frac{4\mathrm{d}}{5}\] is introduced between the plates and the new capacity is C. The ratio \[C:C_{0}\] is ______.
