Advertisements
Advertisements
प्रश्न
A sphercial capacitor is made of two conducting spherical shells of radii a and b. The space between the shells is filled with a dielectric of dielectric constant K up to a radius c as shown in figure . Calculate the capacitance.
उत्तर
We have two capacitors: one made by the shells a and c and the other made by the shells b and c.
The capacitance of the capacitor `C_(ac)` is given by
`C_(ac) = (4pi∈_0acK)/((c-a))`
The capacitance of the capacitor `C_(cb)` is given by
`C_(cb) = (4pi∈_0bcK)/(K(b-c)`
The two capacitors are in series; thus, the equivalent capacitance is given by
`1/C = 1/C_(ac) + 1/C_(cb)`
⇒ `1/C = ((c-a))/(4pi∈_0acK) + ((b-c))/(4pi∈_0cb)`
⇒ `1/C = (b(c-a)+Ka(b-c))/(K4pi∈_0abc)`
⇒ `C = (K4pi∈_0abc)/(b(c-a)+Ka(b-c))`
APPEARS IN
संबंधित प्रश्न
A bulb is connected in series with a variable capacitor and an AC source as shown. What happens to the brightness of the bulb when the key is plugged in and capacitance of the capacitor is gradually reduced?
Define capacitor reactance. Write its S.I units.
Two metal spheres of capacitance C1 and C2 carry some charges. They are put in contact and then separated. The final charges Q1 and Q2 on them will satisfy
When 1⋅0 × 1012 electrons are transferred from one conductor to another, a potential difference of 10 V appears between the conductors. Calculate the capacitance of the two-conductor system.
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?
Find the charge appearing on each of the three capacitors shown in figure .
Find the charge supplied by the battery in the arrangement shown in figure.
Each of the plates shown in figure has surface area `(96/∈_0) xx 10^-12` Fm on one side and the separation between the consecutive plates is 4⋅0 mm. The emf of the battery connected is 10 volts. Find the magnitude of the charge supplied by the battery to each of the plates connected to it.
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.
Find the capacitances of the capacitors shown in figure . The plate area is Aand the separation between the plates is d. Different dielectric slabs in a particular part of the figure are of the same thickness and the entire gap between the plates is filled with the dielectric slabs.
Obtain an expression for equivalent capacitance when three capacitors C1, C2 and C3 are connected in series.
Obtain the expression for capacitance for a parallel plate capacitor.
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.
Five capacitor each of capacitance value C are connected as shown in the figure. The ratio of capacitance between P to R, and the capacitance between P and Q is ______.
Can the potential function have a maximum or minimum in free space?
Two plates A and B of a parallel plate capacitor are arranged in such a way, that the area of each plate is S = 5 × 10-3 m 2 and distance between them is d = 8.85 mm. Plate A has a positive charge q1 = 10-10 C and Plate B has charge q2 = + 2 × 10-10 C. Then the charge induced on the plate B due to the plate A be - (....... × 10-11 )C
A capacitor of capacity 2 µF is charged to a potential difference of 12 V. It is then connected across an inductor of inductance 0.6 mH. The current in the circuit at a time when the potential difference across the capacitor is 6.0 V is ______ × 10-1A.
Current versus time and voltage versus time graphs of a circuit element are shown in figure.
 |
 |
The type of the circuit element is ______.
