Advertisements
Advertisements
प्रश्न
Find the equivalent capacitance of the network shown in the figure, when each capacitor is of 1 μF. When the ends X and Y are connected to a 6 V battery, find out (i) the charge and (ii) the energy stored in the network.
Advertisements
उत्तर
The equivalent circuit is given below.
There are two capacitors in one branch in series. So, the equivalent capacitance of one branch will be
1/1+1/1=2muF
The arrangement will be further reduced to the form given below.
Now, both the capacitors are in parallel, so the equivalent capacitance will be
2+2=4μF
Therefore, the equivalent capacitance is 4 μF.
(i)
Voltage, V = 6 V
The charge in the network is given by
q=CV
Here, C is the equivalent capacitance.
Now,q=4×10−6×6
=24×10−6 C=24 μC
(ii)
The energy stored in the network is given by
E=1/2CV2
=12×4×10−6×(6)2
=12×4×36×10−6
=72×10−6 J
=72 μJ
APPEARS IN
संबंधित प्रश्न
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 _________ .
Suppose, one wishes to construct a 1⋅0 farad capacitor using circular discs. If the separation between the discs be kept at 1⋅0 mm, what would be the radius of the discs?
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.
Find the equivalent capacitance of the infinite ladder shown in figure between the points A and B.
A parallel-plate capacitor of plate area A and plate separation d is charged to a potential difference V and then the battery is disconnected. A slab of dielectric constant K is then inserted between the plates of the capacitor so as to fill the space between the plates. Find the work done on the system in the process of inserting the slab.
Obtain the expression for energy stored in the parallel plate capacitor.
The radius of a sphere of capacity 1 microfarad in the air is ______
A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (U) as ε = αU where α = 2V–1. A similar capacitor with no dielectric is charged to U0 = 78V. It is then connected to the uncharged capacitor with the dielectric. Find the final voltage on the capacitors.
Eight drops of mercury of equal radius and possessing equal charge combine to form a big drop. The capacitance of bigger drop as compared to each small drop is ______.
