A slab of material of dielectric constant k has the same area as the plates of a parallel plate capacitor but has a thickness 3 d 4 . Find the ratio of the capacitance with dielectric inside it to its capacitance without the dielectric.

If V 0 is the potential difference when there is no dielectric, then the electric field between the capacitor plates will be E 0 = V 0 d After the dielectric is inserted, the electric field in the dielectric reduces to E = E 0 k Now the potential difference between the plates will be V = E 0 . d 4 + E . 3 d 4 = E 0 . d 4 + E 0 k . 3 d 4 = E 0 d 1 4 + 3 4 k = V 0 k + 3 4 k Thus the potential difference decreases by a factor of k + 3 4 k , while the free charge q 0 on the plates remains the same. The capacitance increases to a new value given by C = q 0 V = 4 k k + 3 . q 0 V 0 = 4 k k + 3 C 0 C C 0 = 4 k k + 3

A slab of material of dielectric constant k has the same area as the plates of a parallel plate capacitor but has a thickness 3 d 4 . Find the ratio of the capacitance with dielectric inside it to its capacitance without the dielectric.

If V 0 is the potential difference when there is no dielectric, then the electric field between the capacitor plates will be E 0 = V 0 d After the dielectric is inserted, the electric field in the dielectric reduces to E = E 0 k Now the potential difference between the plates will be V = E 0 . d 4 + E . 3 d 4 = E 0 . d 4 + E 0 k . 3 d 4 = E 0 d 1 4 + 3 4 k = V 0 k + 3 4 k Thus the potential difference decreases by a factor of k + 3 4 k , while the free charge q 0 on the plates remains the same. The capacitance increases to a new value given by C = q 0 V = 4 k k + 3 . q 0 V 0 = 4 k k + 3 C 0 C C 0 = 4 k k + 3

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12th CBSE

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A slab of material of dielectric constant $k$ has the same area as the plates of a parallel plate capacitor but has a thickness $\frac{3 d}{4}$ . Find the ratio of the capacitance with dielectric inside it to its capacitance without the dielectric.

Important Questions on Electrostatic Potential and Capacitance

MEDIUM

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 7

Distinguish, with the help of a suitable diagram, the difference in the behaviour of a conductor and a dielectric placed in an external electric field. How does a polarized dielectric modify the original external field?

MEDIUM

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 7

If two similar large plates, each of area

A

having surface charge densities

+ σ

and

- σ

are separated by a distance

d

in air, find the expressions for the field at points between the two plates and on the outer side of the plates. Specify the direction of the field in each case.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 7

If two similar large plates, each of area

A

having surface charge densities

+ σ

and

- σ

are separated by a distance

d

in air, find the expressions for the potential difference between the plates.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 7

If two similar large plates, each of area

A

having surface charge densities

+ σ

and

- σ

are separated by a distance

d

in air, find the expressions for the capacitance of the capacitor so formed.

MEDIUM

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 8

Obtain the expression for the capacitance of a parallel plate capacitor. Three capacitors of capacitances

C_{1}, C_{2}

and

C_{3}

are connected in series. Show that the energy stored in the series combination is the same as that in the parallel combination.

MEDIUM

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 8

Obtain the expression for the capacitance of a parallel plate capacitor. Three capacitors of capacitances

C_{1}, C_{2}

and

C_{3}

are connected in parallel. Show that the energy stored in the series combination is the same as that in the parallel combination.

MEDIUM

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 9

Derive the expression for the energy stored in the parallel plate capacitor. Hence obtain the expression for the energy density of the electric field.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 9

A fully charged parallel plate capacitor is connected across an uncharged identical capacitor. Show that the energy stored in the combination is less than that stored initially in the single capacitor.

A slab of material of dielectric constant k has the same area as the plates of a parallel plate capacitor but has a thickness 3 d4. Find the ratio of the capacitance with dielectric inside it to its capacitance without the dielectric.

Important Questions on Electrostatic Potential and Capacitance

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A slab of material of dielectric constant $k$ has the same area as the plates of a parallel plate capacitor but has a thickness $\frac{3 d}{4}$ . Find the ratio of the capacitance with dielectric inside it to its capacitance without the dielectric.