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
Find the charge on the capacitor as shown in the circuit.
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.
Find the charge on the capacitor shown in the figure.
A 100 μF capacitor is joined to a 24 V battery through a 1.0 MΩ resistor. Plot qualitative graphs (a) between current and time for the first 10 minutes and (b) between charge and time for the same period.
By evaluating ∫i2Rdt, show that when a capacitor is charged by connecting it to a battery through a resistor, the energy dissipated as heat equals the energy stored in the capacitor.
A capacitor of capacitance 100 μF is connected across a battery of emf 6 V through a resistance of 20 kΩ for 4 s. The battery is then replaced by a thick wire. What will be the charge on the capacitor 4 s after the battery is disconnected?
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 point charge Q is placed at the origin. Find the electrostatic energy stored outside the sphere of radius R centred at the origin.
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.
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.
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 ______.
What fraction of the energy drawn from the charging battery is stored in a capacitor?
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.
Electrostatic energy of 4 x 10−4 J is stored in a charged 25 pF capacitor. Find the charge on the capacitor.
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 ______.
