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
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 equivalent capacitance of the combination shown in the figure is _________ .
It is required to construct a 10 µF capacitor which can be connected across a 200 V battery. Capacitors of capacitance 10 µF are available but they can withstand only 50 V. Design a combination which can yield the desired result.
A parallel-plate capacitor has plate area 100 cm2 and plate separation 1⋅0 cm. A glass plate (dielectric constant 6⋅0) of thickness 6⋅0 mm and an ebonite plate (dielectric constant 4⋅0) are inserted one over the other to fill the space between the plates of the capacitor. Find the new capacitance.
Obtain an expression for equivalent capacitance when three capacitors C1, C2 and C3 are connected in series.
Dielectric constant for a metal is ______.
The capacitance of a parallel plate capacitor is 60 µF. If the distance between the plates is tripled and area doubled then new capacitance will be ______.
Two similar conducting spheres having charge+ q and -q are placed at 'd' seperation from each other in air. The radius of each ball is r and the separation between their centre is d (d >> r). Calculate the capacitance of the two ball system ______.
The material filled between the plates of a parallel plate capacitor has a resistivity of 200Ωm. The value of the capacitance of the capacitor is 2 pF. If a potential difference of 40V is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is ______.
(given the value of relative permittivity of a material is 50.)
A capacitor with capacitance 5µF is charged to 5 µC. If the plates are pulled apart to reduce the capacitance to 2 µF, how much work is done?
