Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 11: Problem 1623

Large number of capacitors of rating $10 \mu \mathrm{F} / 200 \mathrm{~V} \mathrm{~V}$ are available. The minimum number of capacitors required to design a \(10 \mu \mathrm{F} / 700 \mathrm{~V}\) capacitor is (A) 16 (B) 8 (C) 4 (D) 7

Short Answer

Expert verified
The minimum number of 10 μF / 200 V capacitors required to design a 10 μF / 700 V capacitor is 16, which can be achieved by connecting 4 sets of series-configured capacitors (each consisting of 4 capacitors) in parallel. The correct answer is (A) 16.

Step by step solution

01

Calculate the required series connection

In order to achieve the desired voltage rating of 700 V, we first need to find the minimum number of capacitors connected in series so that their combined voltage rating is at least 700 V. Since each capacitor has a voltage rating of 200 V, we can calculate this as follows: Number of capacitors in series = \( \frac{Target~Voltage~Rating}{Individual~Capacitor~Voltage~Rating} \) Number of capacitors in series = \( \frac{700}{200} \) Number of capacitors in series = 3.5 Since we can't have half of a capacitor, we need to use 4 capacitors in series. Now, we need to calculate the equivalent capacitance of this series configuration.
02

Calculate the equivalent capacitance of the series configuration

We can calculate the equivalent capacitance (C_eq) of a series configuration using the formula: \(\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + ..... + \frac{1}{C_n}\) In our case, we have 4 capacitors of equal capacitance (10 μF) connected in series, so we can write the formula as: \(\frac{1}{C_{eq}} = 4 \times \frac{1}{10~μF}\)
03

Calculate C_eq

Solving for C_eq by taking the reciprocal of both sides: \(C_{eq} = \frac{10~μF}{4}\) \(C_{eq} = 2.5~μF\) So, when we connect four 10 μF / 200 V capacitors in series, the resulting equivalent capacitance is 2.5 μF with a total voltage rating of 800 V (4 x 200 V).
04

Calculate the parallel connection to achieve desired capacitance

Since we want a 10 μF / 700 V capacitor, we need to connect the series-configured capacitors in parallel to increase the capacitance while maintaining the 700 V rating. We know that the capacitors connected in parallel would have the capacitance added together. Therefore, to achieve 10 μF, we need: Desired capacitance (10 μF) = Number of parallel capacitors × Series capacitance (2.5 μF) Number of parallel capacitors = \( \frac{10~μF}{2.5~μF} \) Number of parallel capacitors = 4 So, to create a 10 μF / 700 V capacitor, we need 4 sets of series-configured capacitors connected in parallel, each of which consists of 4 capacitors.
05

Find the total and minimum number of capacitors required

Now, we can calculate the total and minimum number of capacitors needed to create the desired 10 μF / 700 V capacitor: Total capacitors = Number of parallel capacitors × Number of capacitors in series Total capacitors = 4 × 4 Total capacitors = 16 Thus, the minimum number of 10 μF / 200 V capacitors required to design a 10 μF / 700 V capacitor is 16. The correct answer is (A) 16.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Two identical metal plates are given positive charges \(\mathrm{Q}_{1}\) and \(\mathrm{Q}_{2}\left(<\mathrm{Q}_{1}\right)\) respectively. If they are now brought close to gather to form a parallel plate capacitor with capacitance \(\mathrm{c}\), the potential difference between them is (A) \(\left[\left(Q_{1}+Q_{2}\right) /(2 c)\right]\) (B) \(\left[\left(\mathrm{Q}_{1}+\mathrm{Q}_{2}\right) / \mathrm{c}\right]\) (C) \(\left[\left(\mathrm{Q}_{1}-\mathrm{Q}_{2}\right) /(2 \mathrm{c})\right]\) (D) \(\left[\left(\mathrm{Q}_{1}-\mathrm{Q}_{2}\right) / \mathrm{c}\right]\)

A long string with a charge of \(\lambda\) per unit length passes through an imaginary cube of edge \(\ell\). The maximum possible flux of the electric field through the cube will be ....... (A) \(\sqrt{3}\left(\lambda \ell / \in_{0}\right)\) (B) \(\left(\lambda \ell / \in_{0}\right)\) (C) \(\sqrt{2}\left(\lambda \ell / \in_{0}\right)\) (D) \(\left[\left(6 \lambda \ell^{2}\right) / \epsilon_{0}\right]\)

A \(5 \mu \mathrm{F}\) capacitor is charged by a \(220 \mathrm{v}\) supply. It is then disconnected from the supply and is connected to another uncharged $2.5 \mu \mathrm{F}$ capacitor. How much electrostatic energy of the first capacitor is lost in the form of heat and electromagnetic radiation ? (A) \(0.02 \mathrm{~J}\) (B) \(0.121 \mathrm{~J}\) (C) \(0.04 \mathrm{~J}\) (D) \(0.081 \mathrm{~J}\)

An oil drop of 12 excess electrons is held stationary under a constant electric field of \(2.55 \times 10^{4} \mathrm{Vm}^{-1}\). If the density of the oil is \(1.26 \mathrm{gm} / \mathrm{cm}^{3}\) then the radius of the drop is \(\ldots \ldots \ldots \mathrm{m}\). (A) \(9.75 \times 10^{-7}\) (B) \(9.29 \times 10^{-7}\) (C) \(9.38 \times 10^{-8}\) (D) \(9.34 \times 10^{-8}\)

A parallel plate capacitor has the space between its plates filled by two slabs of thickness \((\mathrm{d} / 2)\) each and dielectric constant \(\mathrm{K}_{1}\) and \(\mathrm{K}_{2}\) If \(\mathrm{d}\) is the plate separation of the capacitor, then capacity of the capacitor is .......... (A) $\left[\left(2 \mathrm{~d} \in_{0}\right) / \mathrm{A}\right]\left[\left(\mathrm{K}_{1}+\mathrm{K}_{2}\right) /\left(\mathrm{K}_{1} \mathrm{~K}_{2}\right)\right]$ (B) $\left[\left(2 \mathrm{~A} \in_{0}\right) / \mathrm{d}\right]\left[\left(\mathrm{K}_{1} \mathrm{~K}_{2}\right) /\left(\mathrm{K}_{1}+\mathrm{K}_{2}\right)\right]$ (C) $\left[\left(2 \mathrm{Ad} \epsilon_{0}\right) / \mathrm{d}\right]\left[\left(\mathrm{K}_{1}+\mathrm{K}_{2}\right) /\left(\mathrm{K}_{1} \mathrm{~K}_{2}\right)\right]$ d] \(\left(K_{1}+K_{2}\right)\) (D) \(\left[\left(2 \mathrm{~A} \in_{0}\right) /\right.\)
See all solutions

Recommended explanations on English Textbooks

Language and Social Groups

Read Explanation

Pragmatics

Read Explanation

Multiple Choice Questions

Read Explanation

International English

Read Explanation

Essay Plan

Read Explanation

Argumentative Essay

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free