Advertisements
Advertisements
प्रश्न
Two conducting spheres of radii R1 and R2 are kept widely separated from each other. What are their individual capacitances? If the spheres are connected by a metal wire, what will be the capacitance of the combination? Think in terms of series−parallel connections.
Advertisements
उत्तर
We need to calculate the capacitance of an isolated charged sphere.
Let us assume that the charge on the sphere is Q and its radius is R.
Capacitance of the charged sphere can be found by imagining a concentric sphere of infinite radius consisting of −Q charge.
Potential difference between the spheres = `1/(4pi∈_0) Q/R` - 0 = `1/(4pi∈_0) Q/R`
Capacitance is the ratio of the magnitude of the charge on each conductor to the potential difference between them.
`C = Q/(1/(4pi∈_0) Q/R` = `4pi∈_0 R`
Therefore, the capacitances of spheres of radii R1 and R2 are C1 and C2, respectively. They are given by
`C_1 = 4pi∈_0 R_1`
`C_2 = 4pi∈_0 R_2`
If the spheres are connected by a metal wire, the charge will flow from one sphere to another till their potentials become the same.
As there potentials become the same, the potential difference between the conductors for both the capacitors also becomes the same. Thus, it can be concluded that the capacitors are connected in parallel.
Thus, the capacitance of the combination is given by `C_(eq) = C_1 + C_2`
= `4pi∈_0(R_1 + R_2)`
APPEARS IN
संबंधित प्रश्न
When an AC source is connected to an ideal capacitor, show that the average power supplied by the source over a complete cycle is zero
Obtain the equivalent capacitance of the network in Figure. For a 300 V supply, determine the charge and voltage across each capacitor.
A capacitor has capacitance C. Is this information sufficient to know what maximum charge the capacitor can contain? If yes, what is this charges? If no, what other information is needed?
The equivalent capacitance of the combination shown in the figure is _________ .
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.
Find the charges on the three capacitors connected to a battery as shown in figure.
Take `C_1 = 2.0 uF , C_2 = 4.0 uF , C_3 = 6.0 uF and V` = 12 volts.
Each capacitor shown in figure has a capacitance of 5⋅0 µF. The emf of the battery is 50 V. How much charge will flow through AB if the switch S is closed?
Find the equivalent capacitance of the infinite ladder shown in figure between the points A and B.
A finite ladder is constructed by connecting several sections of 2 µF, 4 µF capacitor combinations as shown in the figure. It is terminated by a capacitor of capacitance C. What value should be chosen for C, such that the equivalent capacitance of the ladder between the points A and B becomes independent of the number of sections in between?
An air-filled parallel-plate capacitor is to be constructed which can store 12 µC of charge when operated at 1200 V. What can be the minimum plate area of the capacitor? The dielectric strength of air is `3 xx 10^6 "Vm"^-1`
You are provided with 8 μF capacitors. Show with the help of a diagram how you will arrange minimum number of them to get a resultant capacitance of 20 μF.
Three capacitors are connected in a triangle as shown in the figure. The equivalent capacitance between points A and C is ______.
Calculate the resultant capacitances for each of the following combinations of capacitors.
- 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.
Current versus time and voltage versus time graphs of a circuit element are shown in figure.
 |
 |
The type of the circuit element is ______.
Two identical capacitors are connected as shown and have an initial charge of Q0. The separation between the plates of each capacitor is d0. Suddenly the left plate of the upper capacitor and right plate of the lower capacitor start moving with speed v towards the left while the other plate of each capacitor remains fixed. `("given" (Q_0V)/(2d_0) = 10 A)`. The value of current in the circuit is ______ A.
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?
