Advertisements
Advertisements
Question
Capacitors P and Q have identical cross-sectional areas A and separation d. The space between the capacitors is filled with a dielectric of dielectric constant Er as shown in the figure. Calculate the capacitance of capacitors P and Q.
Advertisements
Solution
- The arrangement can be supposed to be a parallel combination of two capacitors each with plate area A/2 and separation. d. Total capacitance `"C"_"p" = "C"_"air" + "C"_"dielectric"`
`= (epsilon_0("A"//2))/"d" + (epsilon_0("A"//2)epsilon"r")/"d"`
`"C"_"p" = (epsilon_0"A")/"2d" (1 + epsilon_"r")` - The arrangement can be supposed to be a series combination of two capacitors, each with plate area A and separation d/2.
Total capacitance CQ = `("C"_1"C"_2)/("C"_1 + "C"_2)`
`= ((2epsilon_0"A")/"d" xx (2epsilon_"r"epsilon_0"A")/"d")/((2epsilon_0"A")/"d" + (2epsilon_"r"epsilon_0"A")/"d")`
`= (4epsilon_"r" ((epsilon_0"A")/"d")^2)/((2epsilon_0"A")/"d" (1 + epsilon_"r"))`
`= (2epsilon_"r" (epsilon_0"A")/"d")/(1 + epsilon_"r")`
`"C"_"Q" = (2epsilon_0"A")/"d" (epsilon_"r"/(1 + epsilon_"r"))`
APPEARS IN
RELATED QUESTIONS
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.
A capacitor of unknown capacitance is connected across a battery of V volts. The charge stored in it is 360 μC. When potential across the capacitor is reduced by 120 V, the charge stored in it becomes 120 μC.
Calculate:
(i) The potential V and the unknown capacitance C.
(ii) What will be the charge stored in the capacitor, if the voltage applied had increased by 120 V?
As `C = (1/V) Q` , can you say that the capacitance C is proportional to the charge Q?
Find the capacitance of the combination shown in figure between A and B.
Consider the situation shown in the figure. The switch S is open for a long time and then closed. (a) Find the charge flown through the battery when the switch S is closed. (b) Find the work done by the battery.(c) Find the change in energy stored in the capacitors.(d) Find the heat developed in the system.
The figure show a network of five capacitors connected to a 10V battery. Calculate the charge acquired by the 5μF capacitor.
Can the potential function have a maximum or minimum in free space?
For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant K is used, which has the same area as the plates of the capacitor.
The thickness of the dielectric slab is `3/4`d, where 'd' is the separation between the plate of the parallel plate capacitor.
The new capacitance (C') in terms of the original capacitance (C0) is given by the following relation:
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 ______.
