Advertisements
Advertisements
प्रश्न
Each capacitor in figure has a capacitance of 10 µF. The emf of the battery is 100 V. Find the energy stored in each of the four capacitors.
Advertisements
उत्तर
Capacitors b and c are in parallel; their equivalent capacitance is 20 µF.
Thus, the net capacitance of the circuit is given by
`1/C_"net" = 1/10 + 1/20 + 1/10`
`⇒ 1/C_"net" = (2+1+2)/20 = 5/20`
`⇒ C_"net" = 4 "uF"`
The total charge of the battery is given by
`Q = C_"net"V = (4 "uF") xx (100 "V") = 4 xx 10^-4 C`
For a and d,
`q = 4 xx 10^-4 "C" and "C" = 10^-5 "F"`
`therefore E = q^2/(2C) = (4 xx 10^-4)/(2 xx 10^-5)`
`⇒ E = 8 xx 10^-3 "J" = 8 "mJ"`
For b and c,
`q = 4 xx 10^-4 "C" and "C"_(eq) = 2"C" = 2 xx 10^-5 "F"`
`therefore V = q/C_(eq) (4 xx 10^-4)/(2 xx 10^-5) = 20 V`
`⇒ E = 1/2 CV^2`
`⇒ E = 1/2 xx 10^-5 xx 400`
`⇒ E = 2 xx 10^-3 "J" = 2 "mJ"`
APPEARS IN
संबंधित प्रश्न
A 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in the capacitor?
Find the ratio of energy stored in the two configurations if they are both connected to the same source.
The energy density in the electric field created by a point charge falls off with the distance from the point charge as
A capacitor C1 of capacitance 1 μF and a capacitor C2 of capacitance 2 μF are separately charged by a common battery for a long time. The two capacitors are then separately discharged through equal resistors. Both the discharge circuits are connected at t = 0.
(a) The current in each of the two discharging circuits is zero at t = 0.
(b) The currents in the two discharging circuits at t = 0 are equal but not zero.
(c) The currents in the two discharging circuits at t = 0 are unequal.
(d) C1 loses 50% of its initial charge sooner than C2 loses 50% of its initial charge.
(a) Find the current in the 20 Ω resistor shown in the figure. (b) If a capacitor of capacitance 4 μF is joined between the points A and B, what would be the electrostatic energy stored in it in steady state?
How many time constants will elapse before the current in a charging RC circuit drops to half of its initial value? Answer the same question for a discharging RC circuit.
A capacitor with stored energy 4⋅0 J is connected with an identical capacitor with no electric field in between. Find the total energy stored in the two capacitors.
A capacitor of capacitance C is given a charge Q. At t = 0, it is connected to an uncharged capacitor of equal capacitance through a resistance R. Find the charge on the second capacitor as a function of time.
A capacitor of capacitance C is given a charge Q. At t = 0, it is connected to an ideal battery of emf ε through a resistance R. Find the charge on the capacitor at time t.
A metal sphere of radius R is charged to a potential V.
- Find the electrostatic energy stored in the electric field within a concentric sphere of radius 2 R.
- Show that the electrostatic field energy stored outside the sphere of radius 2 R equals that stored within it.
Figure shows two identical parallel plate capacitors connected to a battery through a switch S. Initially, the switch is closed so that the capacitors are completely charged. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant 3. Find the ratio of the initial total energy stored in the capacitors to the final total energy stored.
Obtain the expression for the energy stored in a capacitor connected across a dc battery. Hence define energy density of the capacitor
Choose the correct option:
Energy stored in a capacitor and dissipated during charging a capacitor bear a ratio.
If the p. d. across a capacitor is increased from 10 V to 30 V, then the energy stored with the capacitor ____________.
A parallel plate condenser is immersed in an oil of dielectric constant 2. The field between the plates is ______.
A parallel plate capacitor has a uniform electric field ‘`vec "E"`’ in the space between the plates. If the distance between the plates is ‘d’ and the area of each plate is ‘A’, the energy stored in the capacitor is ______
(ε0 = permittivity of free space)
Prove that, if an insulated, uncharged conductor is placed near a charged conductor and no other conductors are present, the uncharged body must be intermediate in potential between that of the charged body and that of infinity.
In a capacitor of capacitance 20 µF, the distance between the plates is 2 mm. If a dielectric slab of width 1 mm and dielectric constant 2 is inserted between the plates, what is the new capacitance?
