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
A capacitor 'C', a variable resistor 'R' and a bulb 'B' are connected in series to the ac mains in circuit as shown. The bulb glows with some brightness. How will the glow of the bulb change if (i) a dielectric slab is introduced between the plates of the capacitor, keeping resistance R to be the same; (ii) the resistance R is increased keeping the same capacitance?
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).
The plates of a parallel-plate capacitor are given equal positive charges. What will be the potential difference between the plates? What will be the charges on the facing surfaces and on the outer surfaces?
A parallel-plate capacitor has plates of unequal area. The larger plate is connected to the positive terminal of the battery and the smaller plate to its negative terminal. Let Q, and Q be the charges appearing on the positive and negative plates respectively.
The following figure shows two capacitors connected in series and joined to a battery. The graph shows the variation in potential as one moves from left to right on the branch containing the capacitors.
The separation between the plates of a charged parallel-plate capacitor is increased. Which of the following quantities will change?
(a) Charge on the capacitor
(b) Potential difference across the capacitor
(c) Energy of the capacitor
(d) Energy density between the plates
Find the charges on the four capacitors of capacitances 1 μF, 2 μF, 3 μF and 4 μF shown in the figure.
Two parallel plate capacitors X and Y, have the same area of plates and same separation between plates. X has air and Y with dielectric of constant 2, between its plates. They are connected in series to a battery of 12 V. The ratio of electrostatic energy stored in X and Y is ______.
Three different capacitors are·connected in series. Then:-
The equivalent capacitance of the combination shown in the figure is ______.
Two equal capacitors are first connected in series and then in parallel The ratio of the equivalent capacities in the two cases will be ______.
The total charge on the system of capacitors C1 = 1 µF, C2 = 2 µF, C3 = 4 µF and C4 = 3 µF connected in parallel is ______. (Assume a battery of 20 V is connected to the combination)
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:
The potential difference that must be applied across the series and parallel combination of 4 identical capacitors such that the energy stored in them becomes the same. The ratio of potential difference in series to parallel combination is ______.
Which formula gives the equivalent capacitance of capacitors in series?
Which formula gives the equivalent capacitance of capacitors in parallel?
Which relation gives the charge on one capacitor in a parallel combination when the common voltage is \[V\]?
