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Chapter 1: Problem 44

The dimensions of emf in MKS is (a) \(\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2} \mathrm{Q}^{-2}\right]\) (b) \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-2} \mathrm{Q}^{-2}\right]\) (c) \(\left[\mathrm{MLT}^{-2} \mathrm{Q}^{-1}\right]\) (d) \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-2} \mathrm{Q}^{-1}\right]\)

Short Answer

Expert verified
The dimensions of EMF in MKS is \([ML^2T^{-2}Q^{-1}]\), which is option (d).

Step by step solution

01

Understanding the Concept of EMF

Electromotive force (EMF) is the energy provided by a source to move a charge through an electric circuit. The unit of EMF in the MKS system is the volt (V), and 1 Volt is equivalent to Joules per Coulomb (J/C). Therefore, we need to derive the dimensions of 1 Joule and 1 Coulomb first.
02

Dimensions of Joule

A Joule (J) is the unit of energy or work in the MKS system. Joules are defined as the work done when a force of 1 Newton is applied over a distance of 1 meter. The dimension of energy (or work) is \([ML^2T^{-2}]\), where \(M\) is mass, \(L\) is length, and \(T\) is time.
03

Dimensions of Coulomb

A Coulomb (C) is the unit of electric charge, and it is defined by the equation for current: \(I = \frac{Q}{T}\), where \(I\) is current. The unit of current is the Ampere (A), which can be expressed as Coulombs per second \(C/s\). Therefore, the dimension of charge \(Q\) is \([Q]\).
04

Calculating Dimensions of EMF

Since EMF is defined in Volts, which can be expressed as Energy (Joules) per Charge (Coulombs), we need to divide the dimensions of Energy by the dimensions of Charge. EMF will have the dimensions: \([ML^2T^{-2}]/[Q]\). This can be simplified to \([ML^2T^{-2}Q^{-1}]\).
05

Identifying the Correct Answer

From our calculation, the dimensions of EMF in the MKS system are \([ML^2T^{-2}Q^{-1}]\). From the given options, this matches option (d).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

MKS System
The MKS system, or Meter-Kilogram-Second system, is one of the key systems of measurement used in physics. This system provides the standard units for various physical quantities, making it easier to compare and compute experimental data across different settings and disciplines. In the MKS system, the unit for length is the meter (m), mass is measured in kilograms (kg), and time is measured in seconds (s).
The simplicity and universality of the MKS system have made it a fundamental part of the International System of Units (SI), which is widely adopted around the globe. It aids in unifying the ways we discuss physical concepts, such as length, area, force, and energy.
Electromotive Force
Electromotive force (EMF) is a physical quantity that reflects the potential to drive electric current through a circuit. It is not a force in the traditional sense, but rather an energy difference per charge that causes free charges to move, generating an electric current. When we talk about the EMF supplied by a battery or a generator, we refer to how much energy that source provides per charge to move it through the circuit.
The unit of electromotive force in the MKS system is the volt (V). A single volt represents one joule of energy supplied per coulomb of charge. Understanding this concept is fundamental to comprehending how electric circuits function and how various electrical devices are powered.
Unit of Energy in Physics
Energy in physics is a measure of the capacity to perform work or produce change. In the MKS system, the unit of energy is the joule (J). A joule is defined as the work done when a force of one newton is applied to move an object one meter. This provides a convenient and consistent way of quantifying energy, making calculations more standardized.
Energy can take many forms, such as kinetic, potential, thermal, electrical, or mechanical energy, depending on the context. Understanding the units of energy helps to better grasp these concepts as well as the principle of energy conservation, which is a cornerstone of physics.
MKS Units Conversion
Conversion between different units in the MKS system is essential for solving a wide variety of physics problems. This often involves converting quantities like energy, force, or time into different units without altering their inherent dimensions. For instance, converting joules to kilojoules simply involves the relationship that 1 kilojoule equals 1000 joules.
Accurate unit conversion is vital in ensuring that calculations remain correct and meaningful. It also helps bridge gaps in understanding between various measurement systems, like converting between MKS units and those of the CGS (Centimeter-Gram-Second) system, often used in more precise scientific contexts. This skill is invaluable for students tackling complex scientific problems.

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Most popular questions from this chapter

The unit of length convenient on the atomic scale is known as an angstrom and is denoted by 脕. \(1 \AA\) \(10^{-10} \mathrm{~m}\). The size of the hydrogen atom is about \(0.5 \mathrm{~A}\). The total atomic volume in \(\mathrm{m}^{3}\) of a mole of hydrogen atoms would be [NCERT] (a) \(3.15 \times 10^{-7} \mathrm{~m}^{3}\) (b) \(3.0 \times 10^{-8} \mathrm{~m}^{3}\) (c) \(3.85 \times 10^{-7} \mathrm{~m}^{3}\) (d) \(2.85 \times 10^{-7} \mathrm{~m}^{3}\)

Dimensions of potential energy are (a) \(\left[\mathrm{MLT}^{-1}\right]\) (b) \(\left[\mathrm{ML}^{2} \mathrm{~T}-2\right]\) (c) \(\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]\) (d) \(\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]\)

The frequency of vibration \(f\) of a mass \(m\) suspended from a spring of spring constant \(k\) is given by relation of the type \(f=c m^{x} k^{y}\), where \(c\) is a dimensionless constant. The values of \(x\) and \(y\) are (a) \(1 / 2,1 / 2\) (b) \(-1 / 2,-1 / 2\) (c) \(1 / 2,-1 / 2\) (d) \(-1 / 2,1 / 2\)

The dimensions of universal gravitational constant are (a) \(\left[\mathrm{ML}^{-3} \mathrm{~T}^{2}\right]\) (b) \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-3}\right]\) (c) \(\left[\mathrm{M}^{-1} \mathrm{~L}^{3} \mathrm{~T}^{-2}\right]\) (d) \(\left[\mathrm{M}^{2} \mathrm{~L}^{2} \mathrm{~T}^{-2}\right]\)

Match the physical quantities given in column I with dimension expressed in terms of mass \((m)\), length \((L)\), time ( \(T\) ) and change \((Q)\) given in column II. Column I \(\quad\) Column II (A) Angular momentum (p) \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]\) (B) Torque (q) \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right.\) ] (C) Inductance (r) \(\left[\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{2} \mathrm{Q}^{2}\right]\) (D) Latent heat (s) \(\left[\mathrm{ML}^{2} \mathrm{Q}^{-2}\right]\) (E) Capacitance (t) \(\left[\mathrm{ML}^{3} \mathrm{~T}^{-1} \mathrm{Q}^{-2}\right]\) (F) Resistivity (u) \(\left[\mathrm{L}^{2} \mathrm{~T}^{-2}\right]\) \(\begin{array}{llllll}\mathrm{A} & \mathrm{B} & \mathrm{C} & \mathrm{D} & \mathrm{E} & \mathrm{F}\end{array}\) (a) q s p t r u (b) q \(\quad \mathrm{p} \quad \mathrm{s} \quad \mathrm{u} \quad \mathrm{r} \quad \mathrm{t}\) (c) p \(\begin{array}{llllll}\text { (c) } & \text { u } & \text { r } & \text { t } & q\end{array}\) (d) \(\mathrm{s} \quad \mathrm{u}\) \(r\) \(\mathrm{t} \quad \mathrm{q} \quad \mathrm{p}\)
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