Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 11: Problem 1627

There are 10 condensers each of capacity \(5 \mu \mathrm{F}\). The ratio between maximum and minimum capacities obtained from these condensers will be (A) \(40: 1\) (B) \(25: 5\) (C) \(60: 3\) (D) \(100: 1\)

Short Answer

Expert verified
The maximum capacity is achieved by connecting all the condensers in parallel, resulting in \(50 \mu F\). The minimum capacity is obtained by connecting all the condensers in series, resulting in \(\frac{1}{2} \mu F\). The ratio between these capacities is \(\frac{50 \mu F}{\frac{1}{2} \mu F} = 100:1\), making the answer option (D).

Step by step solution

01

Find the maximum capacity

To find the maximum capacity, we can connect all the condensers in parallel. In this case, the total capacity is the sum of the individual capacities. As each condenser has a capacity of \(5 \mu F\), the total capacity for all 10 condensers connected in parallel will be: \(C_{max} = 10 \times 5 \mu F = 50 \mu F\)
02

Find the minimum capacity

To find the minimum capacity, we can connect all the condensers in series. In this case, the reciprocal of the total capacity is equal to the sum of the reciprocals of the individual capacities. Thus, \(\frac{1}{C_{min}} = \sum\limits^{10}_{i=1} \frac{1}{C_i}\) As each condenser has a capacity of \(5 \mu F\), we can write: \(\frac{1}{C_{min}} = 10 \times \frac{1}{5 \mu F} = \frac{10}{5 \mu F}\) Now, we can find the minimum capacity by taking the reciprocal of the previous expression: \(C_{min} = \frac{1}{\frac{10}{5 \mu F}} = \frac{5 \mu F}{10} = \frac{1}{2} \mu F\)
03

Find the ratio between maximum and minimum capacities

Now that we have the maximum and minimum capacities, we can determine the ratio between them: Ratio = \(\frac{C_{max}}{C_{min}} = \frac{50 \mu F}{\frac{1}{2} \mu F} = 100 \) Thus, the ratio between maximum and minimum capacities obtained from these condensers is 100:1, which corresponds to option (D).

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 charged spheres of radii \(R_{1}\) and \(R_{2}\) having equal surface charge density. The ratio of their potential is ..... (A) \(\left(\mathrm{R}_{2} / \mathrm{R}_{1}\right)\) (B) \(\left(\mathrm{R}_{2} / \mathrm{R}_{1}\right)^{2}\) (C) \(\left(\mathrm{R}_{1} / \mathrm{R}_{2}\right)^{2}\) (D) \(\left(\mathrm{R}_{1} / \mathrm{R}_{2}\right)\)

Capacitance of a parallel plate capacitor becomes \((4 / 3)\) times its original value if a dielectric slab of thickness \(t=d / 2\) is inserted between the plates (d is the separation between the plates). The dielectric constant of the slab is (A) 8 (B) 4 (C) 6 (D) 2

A ball of mass \(1 \mathrm{gm}\) and charge \(10^{-8} \mathrm{c}\) moves from a point \(\mathrm{A}\), where the potential is 600 volt to the point \(B\) where the potential is zero. Velocity of the ball of the point \(\mathrm{B}\) is $20 \mathrm{~cm} / \mathrm{s}\(. The velocity of the ball at the point \)\mathrm{A}$ will be \(\ldots \ldots\) (A) \(16.8(\mathrm{~m} / \mathrm{s})\) (B) \(22.8(\mathrm{~cm} / \mathrm{s})\) (C) \(228(\mathrm{~cm} / \mathrm{s})\) (D) \(168(\mathrm{~m} / \mathrm{s})\)

Electric charges of \(+10 \mu \mathrm{c}, 5 \mu \mathrm{c},-3 \mu \mathrm{c}\) and \(8 \mu \mathrm{c}\) are placed at the corners of a square of side $\sqrt{2 m}\( the potential at the centre of the square is \)\ldots \ldots$ (A) \(1.8 \mathrm{~V}\) (B) \(1.8 \times 10^{5} \mathrm{~V}\) (C) \(1.8 \times 10^{6} \mathrm{~V}\) (D) \(1.8 \times 10^{4} \mathrm{~V}\)

Three identical spheres each having a charge \(\mathrm{q}\) and radius \(R\), are kept in such a way that each touches the other two spheres. The magnitude of the electric force on any sphere due to other two is \(\ldots \ldots \ldots\) (A) $(\mathrm{R} / 2)\left[1 /\left(4 \pi \epsilon_{0}\right)\right](\sqrt{5} / 4)(\mathrm{q} / \mathrm{R})^{2}$ (B) $\left[1 /\left(8 \pi \epsilon_{0}\right)\right](\sqrt{2} / 3)(\mathrm{q} / \mathrm{R})^{2}$ (C) $\left[1 /\left(4 \pi \epsilon_{0}\right)\right](\sqrt{3} / 4)(\mathrm{q} / \mathrm{R})^{2}$ (D) $-\left[1 /\left(8 \pi \epsilon_{0}\right)\right](\sqrt{3} / 2)(\mathrm{q} / \mathrm{R})^{2}$
See all solutions

Recommended explanations on English Textbooks

Phonology

Read Explanation

Research and Composition

Read Explanation

Discourse

Read Explanation

Creative Story

Read Explanation

Graphology

Read Explanation

Listening and Speaking

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