Advertisements
Advertisements
प्रश्न
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.
उत्तर
- 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
संबंधित प्रश्न
Two capacitors each having capacitance C and breakdown voltage V are joined in series. The capacitance and the breakdown voltage of the combination will be
A thin metal plate P is inserted between the plates of a parallel-plate capacitor of capacitance C in such a way that its edges touch the two plates . The capacitance now becomes _________ .
The capacitance of a capacitor does not depend on
Find the equivalent capacitance of the system shown in figure between the points 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 two square faces of a rectangular dielectric slab (dielectric constant 4⋅0) of dimensions 20 cm × 20 cm × 1⋅0 mm are metal-coated. Find the capacitance between the coated surfaces.
- Charge on each capacitor remains same and equals to the main charge supplied by the battery.
- Potential difference and energy distribute in the reverse ratio of capacitance.
- Effective capacitance is even les than the least of teh individual capacitances.
Can the potential function have a maximum or minimum in free space?
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.
