The space between the plates of a parallel plate capacitor is com… - Vidyadip

Question

The space between the plates of a parallel plate capacitor is completely filled in two ways. In the first case, it is filled with a slab of dielectric constant K. In the second case, it is filled with two slabs of equal thickness and dielectric constants K₁ and K₂ respectively as shown in the figure. The capacitance of the capacitor is same in the two cases. Obtain the relationship between K, K₁ and K₂.

✓

Answer

$\text{C}_1=\frac{\text{K}\varepsilon_0\text{A}}{\text{d}}$

C₂= parallel combination of two capacitors,

$=\frac{\text{K}_1\varepsilon_0\big(\frac{\text{A}}{2}\big)}{\text{d}}+\frac{\text{K}_2\varepsilon_0\big(\frac{\text{A}}{2}\big)}{\text{d}}$

$\frac{\varepsilon_0\text{A}}{2\text{d}}\big(\text{K}_1+\text{K}_2\big)$

$\because\text{C}_1=\text{C}_2$

$\Rightarrow\text{K}=\frac{\text{K}_1+\text{K}_2}{2}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Short Answer Type Questions [2M]" from Electrostatic Potential and Capacitance→Electrostatic Potential and Capacitance — all question types→Physics STD 12 Science question papers→Bihar Board STD 12 Science question papers→Bihar Board question paper generator→

Similar questions

How did Coulomb get the law of electric force between two point charges ?

Answer the following questions: In viewing through a magnifying glass, one usually positions one's eyes very close to the lens. Does angular magnification change if the eye is moved back?

Write and explain the law of conservation of electric charge.

State Bohr’s quantization condition of angular momentum. Calculate the shortest wavelength of the Bracket series and state to which part of the electromagnetic spectrum does it belong.

When a person leaves his home for sightseeing by his car, the meter reads 12352km. When he returns home after two hours the reading is 12416km.

What is the average speed of the car during this period?
What is the average velocity?

Find the increase in mass when 1kg of water is heated from 0^°c to 100^°C. Specific heat capacity of water = 4200J/kg-K.

Find the greatest length of an organ pipe open at both ends that will have its fundamental frequency in the normal hearing range (20Hz-20,000Hz). Speed of sound in air = 340m/s.

A different of 2.3 eV separates two energy levels in an atom. What is the frequency of radiation emitted when the atom make a transition from the upper level to the lower level?

A ferry boat has internal volume 1m³and weight 50kg.

Neglecting the thickness of the wood, find the fraction of the volume of the boat immersed in water.
If aleak develops in the bottom and water starts coming in, what fraction of the boat's volume will be filled with water before water starts coming in from the sides?

Calculate the shortest wavelength in the Balmer series of hydrogen atom. In which region (infra-red, visible, ultraviolet) of hydrogen spectrum does this wavelength lie?