Advertisements
Advertisements
प्रश्न
A capacitor of capacitance 2⋅0 µF is charged to a potential difference of 12 V. It is then connected to an uncharged capacitor of capacitance 4⋅0 µF as shown in figure . Find (a) the charge on each of the two capacitors after the connection, (b) the electrostatic energy stored in each of the two capacitors and (c) the heat produced during the charge transfer from one capacitor to the other.
उत्तर
Charge on the 2 µF capacitor when it is not connected to the 4 µF capacitor is given by
`q = C xx V = 12 xx 2 xx 10^-6`
`⇒ q = 24 xx 10^-6 "C"`
(a) On connecting the capacitors, the charge flows from the 2 µF capacitor to the 4 µF capacitor.
Now, let the charges on the 2 µF and 4 µF capacitors be q1 and q2, respectively.
As they are connected in parallel, the potential difference across them is the same.
`therefore V = q_1/C_1 = q_2/C_2`
`⇒ V = q_1/2 = q_2/4`
`⇒ q_2 = 2 q_1`
The total charge on the capacitors will be the same as the initial charge stored on the 2 µF capacitor.
`therefore q_1 + q_2 = 24 xx 10^-6`
`⇒ 3 q_1 = 24 xx 10^-6 C`
`⇒ q_1 = 8 xx 10^-6 C = 8 muC`
`⇒ q_1 = 2 q_1 = 16 muC`
(b) Energies stored in the capacitors are given by
`E_1 = 1/2 xx q_1^2/C_1 = 16 muJ`
and
`E_2 = 1/2 xx q_2^2/C_2 = 32 muJ`
(c) Initial energy stored in the 2 µF capacitor is given by
`E_i = 1/2 CV^2 = 1/2 xx (2 xx 10^-6) (12)^2`
`⇒ E_i = 144 muJ`
Total energy of the capacitors after they are connected in parallel is given by
Ef = E1 + E2
⇒ Ef = 16 + 32 = 48 μJ
Heat produced during the charge transfer is given by
`E = E_f - E_i`
`⇒ E = 144 - 48 = 96 muJ`
APPEARS IN
संबंधित प्रश्न
Obtain the equivalent capacitance of the network in Figure. For a 300 V supply, determine the charge and voltage across each capacitor.
Two identical parallel plate capacitors A and B are connected to a battery of V volts with the switch S closed. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant K. Find the ratio of the total electrostatic energy stored in both capacitors before and after the introduction of the dielectric.
The equivalent capacitance of the combination shown in the figure is _________ .
A thin metal plate P is inserted between the plates of a parallel-plate capacitor of capacitance C in such a way that its edges touch the two plates . The capacitance now becomes _________ .
When 1⋅0 × 1012 electrons are transferred from one conductor to another, a potential difference of 10 V appears between the conductors. Calculate the capacitance of the two-conductor system.
The outer cylinders of two cylindrical capacitors of capacitance 2⋅2 µF each, are kept in contact and the inner cylinders are connected through a wire. A battery of emf 10 V is connected as shown in figure . Find the total charge supplied by the battery to the inner cylinders.
Find the equivalent capacitance of the system shown in figure between the points a and b.
Find the equivalent capacitance of the infinite ladder shown in figure between the points A and B.
Each of the plates shown in figure has surface area `(96/∈_0) xx 10^-12` Fm on one side and the separation between the consecutive plates is 4⋅0 mm. The emf of the battery connected is 10 volts. Find the magnitude of the charge supplied by the battery to each of the plates connected to it.
The two square faces of a rectangular dielectric slab (dielectric constant 4⋅0) of dimensions 20 cm × 20 cm × 1⋅0 mm are metal-coated. Find the capacitance between the coated surfaces.
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.
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.
Obtain the expression for capacitance for a parallel plate capacitor.
Obtain the expression for energy stored in the parallel plate capacitor.
Derive the expression for resultant capacitance, when the capacitor is connected in series.
Two spherical conductors A and B of radii a and b(b > a) are placed concentrically in the air. B is given a charge +Q and A is earthed. The equivalent capacitance of the system is ______.
Two plates A and B of a parallel plate capacitor are arranged in such a way, that the area of each plate is S = 5 × 10-3 m 2 and distance between them is d = 8.85 mm. Plate A has a positive charge q1 = 10-10 C and Plate B has charge q2 = + 2 × 10-10 C. Then the charge induced on the plate B due to the plate A be - (....... × 10-11 )C
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 ______.
Two identical capacitors are connected as shown and have an initial charge of Q0. The separation between the plates of each capacitor is d0. Suddenly the left plate of the upper capacitor and right plate of the lower capacitor start moving with speed v towards the left while the other plate of each capacitor remains fixed. `("given" (Q_0V)/(2d_0) = 10 A)`. The value of current in the circuit is ______ A.
