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?
In the following arrangement of capacitors, the energy stored in the 6 µF capacitor is E. Find the value of the following :
(i) Energy stored in 12 µF capacitor.
(ii) Energy stored in 3 µF capacitor.
(iii) Total energy drawn from the battery.
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 of capacitance 500 μF is connected to a battery through a 10 kΩ resistor. The charge stored in the capacitor in the first 5 s is larger than the charge stored in the next.
(a) 5 s
(b) 50 s
(c) 500 s
(d) 500 s
How many time constants will elapse before the charge on a capacitors falls to 0.1% of its maximum value in a discharging RC circuit?
Two capacitors of capacitances 4⋅0 µF and 6⋅0 µF are connected in series with a battery of 20 V. Find the energy supplied by the battery.
A capacitor of capacitance C is connected to a battery of emf ε at t = 0 through a resistance R. Find the maximum rate at which energy is stored in the capacitor. When does the rate have this maximum value?
A capacitance C charged to a potential difference V is discharged by connecting its plates through a resistance R. Find the heat dissipated in one time constant after the connections are made. Do this by calculating ∫ i2R dt and also by finding the decrease in the energy stored in the capacitor.
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 large conducting plane has a surface charge density `1.0 xx 10^-4 "Cm"^-2` . Find the electrostatic energy stored in a cubical volume of edge 1⋅0 cm in front of the plane.
Obtain the expression for the energy stored in a capacitor connected across a dc battery.
Choose the correct option:
Energy stored in a capacitor and dissipated during charging a capacitor bear a ratio.
A capacitor is a device that stores ____________.
A parallel plate condenser is immersed in an oil of dielectric constant 2. The field between the plates is ______.
An air-filled parallel plate capacitor has a uniform electric field `overset(->)("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 ______
(∈0 = 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.
A fully charged capacitor C with initial charge q0 is connected to a coil of self-inductance L at t = 0. The time at which the energy is stored equally between the electric and magnetic fields is ______.
A parallel combination of two capacitors of capacities ‘C’ and ‘`C/3`’ respectively is connected across a battery of 12 volt. When both capacitors are fully charged, the charge and energy stored in them is Q1, Q2 and E1, E2 respectively. Then the ratio of (E1 − E2) to (Q1 − Q2) is ______.
