An electrical technician requires a capacitance of 2μF in a circu… - Vidyadip

Question

An electrical technician requires a capacitance of 2μF in a circuitacross a potential difference of 1kV. A large number of 1μF capacitors are available to him each of which can withstand a potential difference of not more than 400V. Suggest a possible arrangement that requires the minimum number of capacitors.

✓

Answer

Total required capacitance, C = 2μF Potential difference, V = 1kV = 1000V Capacitance of each capacitor, C₁ = 1μF

Each capacitor can withstand a potential difference, V₁ = 400V

$\frac{1000}{400}={2.5}$

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 1000V and potential difference across each capacitor must be 400V. Hence, number of capacitors in each row is given as,

Hence, there are three capacitors in each row.

Capacitance of each row $=\frac{1}{1+1+1}=\frac{1}{3}\ \mu \text{F}\ \frac{1}{3}+\frac{1}{3}+\frac{1}{3}+ .....\text{n terms,}$

However, capacitance of the ciruit is given as 2μF.

$\therefore\ \frac{\text{n}}{3}={2}$

N = 6

Let there are n rows, each having three capacitors, which are connected in parallel. Hence,equivalent capacitance of the circuit is given as,

Hence, 6 rows of three capacitors are present in the circuit. A minimum of 6 × 3 i.e., 18capacitors are required for the given arrangement.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Electrostatic Potential and Capacitance→Electrostatic Potential and Capacitance — all question types→Physics STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

A circular disc of radius 'R' is placed co-axially and horizontally inside an opaque hemispherical bowl of radius 'a' (Fig). The far edge of the disc is just visible when viewed from the edge of the bowl. The bowl is filled with transparent liquid of refractive index μ and the near edge of the disc becomes just visible. How far below the top of the bowl is the disc placed?

For the $\beta^{+}$ (positron) emission from a nucleus, there is another competing process known as electron capture (electron from an inner orbit, say, the K–shell, is captured by the nucleus and a neutrino is emitted).
$\text{e}^{+}+^{\text{A}}_{\text{Z}}\text{X}\rightarrow\ ^{\text{A}}_{\text{Z}-1}\text{Y}+\text{v}$
Show that if $\beta^{+}$ emission is energetically allowed, electron capture is necessarily allowed but not vice–versa.

The temperature and pressure at Simla are 15.0°C and 72.0cm of mercury and at Kalka these are 35.0°C and 76.0cm of mercury. Find the ratio of air density at Kalka to the air density at Simla.

Through what potential difference should an electron be accelerated to give it a speed of:

0.6c
0.9c
0.99c

Five long wires A, B, C, D and E, each carrying current I are arranged to form edges of a pentagonal prism as shown in Fig. Each carries current out of the plane of paper.

What will be magnetic induction at a point on the axis O? Axis is at a distance R from each wire.
What will be the field if current in one of the wires (say A) is switched off?
What if current in one of the wire (say) A is reversed?

Consider the situation shown in figure. All the surfaces are frictionless and the string and the pulley are light. Find the magnitude of the acceleration of the two blocks.

A torsional pendulum consists of a solid disc connected to a thin wire$\Big(\alpha=2.4\times10^{-5}\ ^\circ\text{C}^{-1}\Big)$at its centre. Find the percentage change in the time period between peak winter (5^°C) and peak summer (45^°C).

Define the term drift velocity.
On the basis of electron drift, derive an expression for resistivity of a conductor in terms of number density of free electrons and relaxation time. On what factors does resistivity of a conductor depend?
Why alloys like constantan and manganin are used for making standard resistors?

Explain the formation of depletion layer and potential barrier in a p-n junction.
In the figure given below the input waveform is converted into the output waveform by a device ‘X’. Name the device and draw its circuit diagram.

Identify the logic gate represented by the circuit as shown and write its truth table.

A ball falls on an inclined plane of inclination $\theta$ from a height h above the point of impact and makes a perfectly elastic collision. Where will it hit the plane again?