Advertisements
Advertisements
प्रश्न
An electrical technician requires a capacitance of 2 µF in a circuit across a potential difference of 1 kV. A large number of 1 µF capacitors are available to him each of which can withstand a potential difference of not more than 400 V. Suggest a possible arrangement that requires the minimum number of capacitors.
Advertisements
उत्तर
Total required capacitance, C = 2 µF
Potential difference, V = 1 kV = 1000 V
Capacitance of each capacitor, C1 = 1µF
Each capacitor can withstand a potential difference, V1 = 400 V
Suppose a number of capacitors are connected in series and these series circuits are connected in parallel (row) to each other. The potential difference across each row must be 1000 V and the potential difference across each capacitor must be 400 V. Hence, the number of capacitors in each row is given as
`1000/400 = 2.5`
Hence, there are three capacitors in each row.
Capacitance of each row
= `1/(1 + 1 + 1)`
= `1/3 mu "F"`
Let there are n rows, each having three capacitors, which are connected in parallel. Hence, equivalent capacitance of the circuit is given as
`1/3 + 1/3 + 1/3 +.................. "n terms"`
= `"n"/3`
However, the capacitance of the circuit is given as 2 `mu"F"`
∴ `"n"/3 = 2`
n = 6
Hence, 6 rows of three capacitors are present in the circuit. A minimum of 6 × 3 i.e., 18 capacitors are required for the given arrangement.
APPEARS IN
संबंधित प्रश्न
The electric field inside a parallel plate capacitor is E. Find the amount of work done in moving a charge q over a closed loop a b c d a.
Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel. Determine the charge on each capacitor if the combination is connected to a 100 V supply.
A cylindrical capacitor has two co-axial cylinders of length 15 cm and radii 1.5 cm and 1.4 cm. The outer cylinder is earthed and the inner cylinder is given a charge of 3.5 µC. Determine the capacitance of the system and the potential of the inner cylinder. Neglect end effects (i.e., bending of field lines at the ends).
A circuit is set up by connecting inductance L = 100 mH, resistor R = 100 Ω and a capacitor of reactance 200 Ω in series. An alternating emf of \[150\sqrt{2}\] V, 500/π Hz is applies across this series combination. Calculate the power dissipated in the resistor.
Each plate of a parallel plate capacitor has a charge q on it. The capacitor is now connected to a batter. Now,
(a) the facing surfaces of the capacitor have equal and opposite charges
(b) the two plates of the capacitor have equal and opposite charges
(c) the battery supplies equal and opposite charges to the two plates
(d) the outer surfaces of the plates have equal charges
A parallel-plate capacitor is connected to a battery. A metal sheet of negligible thickness is placed between the plates. The sheet remains parallel to the plates of the capacitor.
A wire of resistance ‘R’ is cut into ‘n’ equal parts. These parts are then connected in parallel with each other. The equivalent resistance of the combination is:
Three capacitors each of 4 µF are to be connected in such a way that the effective capacitance is 6µF. This can be done by connecting them:
Three different capacitors are·connected in series. Then:-
Capacitors connected in series have ______
In the circuit shown in figure, initially K1 is closed and K2 is open. What are the charges on each capacitors.
Then K1 was opened and K2 was closed (order is important), What will be the charge on each capacitor now? [C = 1µF]
Two charges q1 and q2 are placed at (0, 0, d) and (0, 0, – d) respectively. Find locus of points where the potential a zero.
The capacitors, each of 4 µF are to be connected in such a way that the effective capacitance of the combination is 6 µF. This can be achieved by connecting ______.
A capacitor of capacity C1 is charged to the potential of V0. On disconnecting with the battery, it is connected with an uncharged capacitor of capacity C2 as shown in the adjoining figure. Find the ratio of energies before and after the connection of switch S.
Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel. What is the total capacitance of the combination?
In the following circuit, the equivalent capacitance between terminal A and terminal B is:
The equivalent capacitance of the combination shown is:
