Basic Electricity MCQ Quiz - Objective Question with Answer for Basic Electricity - Download Free PDF

Explanation:

SI Unit of Electrical Conductance: Siemens (S)

Definition: The Siemens (S) is the derived unit of electrical conductance in the International System of Units (SI). It is named after the German inventor and industrialist Ernst Werner von Siemens. Electrical conductance is the reciprocal of electrical resistance and represents how easily electricity flows through a material. The higher the conductance, the lower the resistance, and vice versa.

SI Base Units of Siemens (S):

To express Siemens in terms of SI base units, we start with its relationship to electrical resistance, which is measured in ohms (Ω). The SI unit of resistance, the ohm (Ω), is defined as one volt per ampere (Ω = V/A). Since conductance is the reciprocal of resistance, the unit of conductance (Siemens) is the reciprocal of the ohm.

Relationship: 1 S = 1 Ω^-1

In terms of SI base units, the ohm can be expressed as follows:

Ω = V/A

Where:

• V (volt) is the SI unit of electric potential, which can be expressed as kg m² s^-3 A^-1
• A (ampere) is the SI unit of electric current

Thus, the ohm can be rewritten in terms of SI base units:

Ω = kg m² s^-3 A^-1 / A

Simplifying this, we get:

Ω = kg m² s^-3 A^-2

Since Siemens (S) is the reciprocal of ohms (Ω), we take the reciprocal of the above expression:

1 S = (kg m² s^-3 A^-2)^-1

On taking the reciprocal, we get:

S = kg^-1 m^-2 s³ A²

This matches with Option 1. Therefore, the correct option is:

Option 1: kg^-1 m^-2 s³ A²

Important Information

To further understand the analysis, let’s evaluate the other options:

Option 2: kg m² s^-3 A^-1

This option represents the SI base unit for voltage (V), not electrical conductance. The voltage can be expressed as kg m² s^-3 A^-1. Therefore, this option is incorrect.

Option 3: kg m² s^-3 A^-2

This option represents the SI base unit for electrical resistance (Ω), which is the reciprocal of electrical conductance. Therefore, this option is also incorrect.

Option 4: kg^-1 m² s³ A²

This option seems to be incorrect as it does not represent any standard physical quantity in SI base units correctly related to electrical conductance. It appears to be a misplaced expression.

Conclusion:

Understanding the SI base units for derived units like Siemens is crucial for accurately describing physical quantities in scientific and engineering contexts. The Siemens (S) is the unit of electrical conductance and is expressed in SI base units as kg^-1 m^-2 s³ A². This understanding helps in various applications, including electrical engineering and physics, where precise measurements and calculations of conductance are essential.

Explanation:

Understanding the SI Base Unit Derived from Ampere

Definition of Ampere: The ampere (A) is the base unit of electric current in the International System of Units (SI). It is defined based on the force between two parallel conductors carrying an electric current. Specifically, one ampere is the constant current that, if maintained in two straight parallel conductors of infinite length and negligible circular cross-section, and placed one meter apart in a vacuum, would produce a force equal to 2 × 10^-7 newton per meter of length.

Understanding the Derived Unit - Coulomb:

The SI base unit directly derived from the definition of the ampere is the coulomb (C). The coulomb is the unit of electric charge and is defined as the amount of charge transported by a constant current of one ampere in one second. In other words, one coulomb is equivalent to the charge transported by one ampere of current flowing for one second.

Mathematical Relationship:

The relationship between the ampere and the coulomb can be expressed mathematically as:

Q = I × t

Where:

• Q is the electric charge in coulombs (C).
• I is the electric current in amperes (A).
• t is the time in seconds (s).

From this equation, it is evident that the coulomb is derived from the ampere, as one coulomb is the amount of charge that flows when a current of one ampere is sustained for one second.

• From the given options, an element which stores energy in the form of a magnetic field is Inductor.
• Circuits containing only resistive element has no transients because resistors don’t store energy in any form.
• Resistor dissipates energy in form of heat coming from I²R loss.
• Inductor stores energy in the form of the magnetic field.
• Capacitor stores energy in the form of the electric field.
• So that transients are present in the inductor & capacitor.

Concept

The power across the battery is given by:

\(P={V^2\over R}\)

where, P = Power

R = Resistance

V = Voltage

Calculation

Given, P = 93 W

R = 1.51Ω

\(93={V^2\over 1.51}\)

V = 11.9 volts

The correct answer is "option 4"

Concept:

• These material are used to manufacture the filaments for incandescent lamp, heating elements for electric heaters and furnaces, space heaters and electric irons etc.The following properties are required in high resistivity or low conductivity conducting material:
  • High resistivity.
  • High melting point.
  • High mechanical strength.
  • High ductility, so that can be drawn in the form of wire easily.
  • High corrosion resistance mean free from oxidation.
  • Low cost.
  • Long life or durable.
  • High flexibility.
• Examples are:
  • Tungsten.
  • Carbon.
  • Nichrome or Brightray B.
  • Nichrome V or Brightray C.
  • Manganin.
• Tungsten:
  • Very hard.
  • Resistivity is twice to aluminum.
  • High tensile strength.
  • Can be drawn in the form of very thin wire.
  • Oxidize very quickly in the presence of oxygen.
  • Can be used up to 2000 deg C in the atmosphere of inert gases (Nitrogen, Argon etc.) without oxidation.

Concept:

The energy is given by:

\(E=P\times t\)

\(E=(V\times I)\times t\)

where, I = Current

R = Resistance

t = Time

Calculation:

Given, V = 220 V

E = 1.5 kW

t = 1 hr

\(1.5\times 10^3=220\times I\times 1\)

I = 6.82 A

The analogy between Electric Circuit and Magnetic Circuit:

Dependent sources depend on some other quantity and these can be classified into four types:

1) Voltage Controlled Voltage Source (VCVS)

2) Voltage Controlled Current Source (VCCS)

3) Current Controlled Voltage Source (CCVS)

4) Current Controlled Current Source (CCCS)

The correct answer is option 4): (0.02/° C)

Concept:

The temperature coefficient of resistance is generally defined as the change in electrical resistance of a substance with respect to per degree change in temperature

R_T = R₀ [1+ α (∆T)]

 The change in electrical resistance of any substance due to temperature depends mainly on three factors –

1. The value of resistance at an initial temperature.
2. The rise in temperature.
3. The temperature coefficient of resistance α.

Calculation:

\(\frac{\Delta R}{R_0} = α × \Delta T\)

∆T = 20° C

R_T = \(140\over 100\) R0

∆R = RT - R0

=  \(140\over 100\) R0 - R0

= ​\(40\over 100\)R0

\(\frac{\Delta R}{R_0} = α × \Delta T\)

\(40\over 100\) = α × 20

α  = 0.02/° C

Passive Element:

• The element which receives or absorbs energy and then either converts it into heat (R) or stored it in an electric (C) or magnetic (L) field is called passive element
• Do not need any form of electrical power to operate
• Not able to control the flow of charge
• Cannot amplify, oscillate, or generate an electrical signal
• Used for energy storage, discharge, oscillating, filtering and phase shifting applications
• Examples: Resistor, inductor, capacitor

Important:

Active Element:

• The elements that supply energy to the circuit is called an active element
• These have an ability to control the flow of charge
• Used for current control and voltage control applications
• Examples: Battery, voltage source, current source, diode

Ohm’s law: Ohm’s law states that at a constant temperature, the current through a conductor between two points is directly proportional to the voltage across the two points.

Voltage = Current × Resistance

V = I × R

V = voltage, I = current and R = resistance

The SI unit of resistance is ohms and is denoted by Ω.

It helps to calculate the power, efficiency, current, voltage, and resistance of an element of an electrical circuit.

Limitations of ohms law:

• Ohm’s law is not applicable to unilateral networks. Unilateral networks allow the current to flow in one direction. Such types of networks consist of elements like a diode, transistor, etc.
• Ohm’s law is also not applicable to non – linear elements. Non-linear elements are those which do not have current exactly proportional to the applied voltage that means the resistance value of those elements changes for different values of voltage and current. An example of a non-linear element is thyristor.
• Ohm’s law is also not applicable to vacuum tubes.

 ⇒ According to ohm's law, the Potential difference is directly proportional to the Current.

 ⇒ V œ I

 ⇒ V = IR ,where R is constant (Resistance)

⇒ V' =1/2 V then I' = 1/2 I

 ⇒ if the potential difference gets half then the current is also getting half.

Ohm’s law: Ohm’s law states that at a constant temperature, the current through a conductor between two points is directly proportional to the voltage across the two points.

Voltage = Current × Resistance

V = I × R

V = voltage, I = current and R = resistance

The SI unit of resistance is ohms and is denoted by Ω.

It helps to calculate the power, efficiency, current, voltage, and resistance of an element of an electrical circuit.

It an element follows the ohm’s law, then the element is known as a linear element.

Ex: Resistor

Limitations of ohms law:

• Ohm’s law is not applicable to unilateral networks. Unilateral networks allow the current to flow in one direction. Such types of networks consist of elements like a diode, transistor, etc.
• Ohm’s law is also not applicable to non – linear elements. Non-linear elements are those which do not have current exactly proportional to the applied voltage that means the resistance value of those elements’ changes for different values of voltage and current. An example of a non-linear element is thyristor.
• Ohm’s law is also not applicable to vacuum tubes.

Kirchoff's Laws:

• Kirchhoff’s laws are used for voltage and current calculations in electrical circuits.
• These laws can be understood from the results of the Maxwell equations in the low-frequency limit.
• They are applicable for DC and AC circuits at low frequencies where the electromagnetic radiation wavelengths are very large when we compare with other circuits. So they are only applicable for lumped parameter networks.

Kirchhoff's current law (KCL) is applicable to networks that are:

• Unilateral or bilateral 
• Active or passive 
• Linear or non-linear
• Lumped network

KCL (Kirchoff Current Law): 

According to Kirchhoff’s current law (KCL), the algebraic sum of the electric currents meeting at a common point is zero.

Mathematically we can express this as:

\(\mathop \sum \limits_{n = 1}^M {i_n} = 0\)

Where in represents the nth current

M is the total number of currents meeting at a common node.

KCL is based on the law of conservation of charge.

Kirchhoff’s Voltage Law (KVL):

It states that the sum of the voltages or electrical potential differences in a closed network is zero. 

Mathematically we can express this as:

\(\mathop \sum \limits_{n = 1}^M {V_n} = 0\)

Where Vn represents the nth Voltage

M is the total number of voltage element.

KVL is based on the law of conservation of energy.