Advertisements
Advertisements
प्रश्न
For the given capacitor configuration
- Find the charges on each capacitor
- potential difference across them
- energy stored in each capacitor.
Advertisements
उत्तर
Capacitor b and c in parallel combination
Cp = Cb + Cc = (6 + 2) μF = 8 μF
Capacitor a, cp and d are in series combination, so the resulatant copacitance
`1/"C"_"s" = 1/"C"_"a" + 1/"C"_"cp" + 1/"C"_"d"`
`= 1/8 + 1/8 + 1/8 = 3/8`
`"C"_"s" = 8/3` μF
- Charge on each capacitor,
Charge on capacitor a, Qa = Cs V = `8/3 xx 9`
Qa = 24 μC
Charge on capacitor, d, Qd = Cs V = `8/3 xx 9`
Qd = 24 μC
Capacitor b and c in parallel
Charge on capacitor, b, Qb = `6/3 xx 9` = 18
Qb = 18 μC
Charge on capacitor, c, Qc = `2/3 xx 9` = 6
Qc = 6 μC - Potential difference across each capacitor, V = `"q"/"c"`
Capacitor Ca, Va = `"q"_"a"/"C"_"a" = (24 xx 10^6)/(8 xx 10^6)` = 3 V
Capacitor Cb, Vb = `"q"_"b"/"C"_"b" = (18 xx 10^6)/(6 xx 10^6)` = 3 V
Capacitor Cc, Vc = `"q"_"c"/"C"_"c" = (6 xx 10^6)/(2 xx 10^6)` = 3 V
Capacitor Cd, Vd = `"q"_"d"/"C"_"d" = (24 xx 10^6)/(8 xx 10^6)` = 3 V - Energy stores in a capacitor, U = `1/2` CV2
Energy in capacitor Ca, Ua = `1/2 "C"_"a" "V"_"a"^2 = 1/2 xx 8 xx 10^-6 xx (3)^2`
Ua = 36 μJ
Capacitor Cb, Ub = `1/2 "C"_"b" "V"_"b"^2 = 1/2 xx 6 xx 10^-6 xx (3)^2`
Ua = 27 μJ
Cc, Uc = `1/2 "C"_"c" "V"_"c"^2 = 1/2 xx 2 xx 10^-6 xx (3)^2`
Ua = 9 μJ
Cd, Ud = `1/2 "C"_"d" "V"_"d"^2 = 1/2 xx 8 xx 10^-6 xx (3)^2`
Ua = 36 μJ
APPEARS IN
संबंधित प्रश्न
(i) Find equivalent capacitance between A and B in the combination given below. Each capacitor is of 2 µF capacitance.
(ii) If a dc source of 7 V is connected across AB, how much charge is drawn from the source and what is the energy stored in the network?
A capacitor of capacitance ‘C’ is being charged by connecting it across a dc source along with an ammeter. Will the ammeter show a momentary deflection during the process of charging? If so, how would you explain this momentary deflection and the resulting continuity of current in the circuit? Write the expression for the current inside the capacitor.
The capacitance of a capacitor does not depend on
A parallel-plate capacitor has plate area 25⋅0 cm2 and a separation of 2⋅00 mm between the plates. The capacitor is connected to a battery of 12⋅0 V. (a) Find the charge on the capacitor. (b) The plate separation is decreased to 1⋅00 mm. Find the extra charge given by the battery to the positive plate.
Find the charge appearing on each of the three capacitors shown in figure .
Find the equivalent capacitance of the system shown in figure between the points a and b.
A cylindrical capacitor is constructed using two coaxial cylinders of the same length 10 cm and of radii 2 mm and 4 mm. (a) Calculate the capacitance. (b) Another capacitor of the same length is constructed with cylinders of radii 4 mm and 8 mm. Calculate the capacitance.
A 5⋅0 µF capacitor is charged to 12 V. The positive plate of this capacitor is now connected to the negative terminal of a 12 V battery and vice versa. Calculate the heat developed in the connecting wires.
A parallel-plate capacitor of capacitance 5 µF is connected to a battery of emf 6 V. The separation between the plates is 2 mm. (a) Find the charge on the positive plate. (b) Find the electric field between the plates. (c) A dielectric slab of thickness 1 mm and dielectric constant 5 is inserted into the gap to occupy the lower half of it. Find the capacitance of the new combination. (d) How much charge has flown through the battery after the slab is inserted?
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.
