Electrical Resistance:– The property of a conductor which opposes the flow of electric current through it is known as resistance.

R = V/I

Conductance:- The property of a conductor which conducts the flow of current through it is called conductance. In other words, conductance is the reciprocal of resistance. Its symbol is G (G= I /R) and its unit is mho represented by ℧.

Reluctance:- Flux in a magnetic circuit also depends on the opposition that the circuit presents to it. Reluctance (R_M), is the opposition a magnetic circuit offers to the formation of magnetic flux.

Permeance:- The reciprocal of reluctance is called permeance and is a measure of the readiness with which the magnetic flux is developed. it is analogous to conductance in an electric circuit and is measured by Weber/ampere-turn.

Permeance = 1/Reluctance

∴ Permeance = flux ⁄ m.m.f

Given

Resistance P = 12 W

Current I = 2 A

Power dissipated by the resistor is

P = I²R

12 = 2² × R

R = 3 Ω

The resistivity of the conductor is defined as

Where A = cross-section area of the conductor = πr² = π × 0.1²

R = Resistance of the conductor = ?

L = Length of the conductor = 4 m

ρ = Resistivity = 0.4 Ω-m

∴ 0.4 = π × 0.1² × R ⁄ 4

R = 50.92 ≅ 51 Ω

When an electric field is applied to a conductor, there occurs a large-scale physical movement of free electrons because these are available in large numbers in Conductor. The resistivity of the conductor is 10⁻⁸ to 10⁻⁶.

On the other hand, if an electric field is applied to an insulator, there is hardly any movement of free electrons because these are just not available in an insulator. Plastics, wood, and rubber are examples of good insulators. Pure water is also an insulator. Tap water, however, contains salts that form ions that can move through the liquid, making it a good conductor.

The insulator is also called the dielectric. There are practically no free electrons in the dielectric. The electrons in dielectric normally remain bound to their respective molecules. The resistivity of the insulator is 10⁷ to 10²³.

Note:-

There are some materials, called semiconductors, which are intermediate between conductors and insulators. The resistivity of the conductor is 10⁻⁶ to 10⁷.

Superconducting materials are materials that conduct electricity without resistance below a certain temperature. Superconductivity is one of the most exciting phenomena in Physics, because of its peculiar nature and its wide application of this phenomenon.

This phenomenon of superconductivity was first discovered by a Dutch physicist, H.K. Onnes. Superconducting materials are having very good electrical and magnetic properties. Before the discovery of superconductors, it is believed that the electrical resistivity of the material becomes zero, only at the absolute temperature.

Every superconductor has zero resistivity, i.e. infinite conductivity, for a small-amplitude of dc current at any temperature below T_c

To identify whether the Inductance is connected in series or in parallel consider the following method

• Use one color for each continuous wire
• DO NOT cross any circuit elements
• Any element that shares the same two colors are in parallel

As you can see from the above figure the three inductances L₁, L₂, L₃ each share two common colors i.e Red and Purple hence these three inductances are connected in parallel.

L₁ ||  L₂ || L₃  = 20 || 30 || 50

= ( 20 × 30) ⁄ (20 + 30) || 50

= 12 || 50 = ( 12 × 50) ⁄ (12 + 50)

L = 9.67

Now the inductance L and L₄ are connected in series

Leq = L + L₄ = 9.67 + 40 = 49.68 ≅ 50 mH

Given

Voltage V = 220 V

Resistance R = 100 ohms

Power consumed by the lamp

P = V²/R = 220²/100

P = 484 Watt

Consider the parallel plate capacitor connected to the battery as shown in the figure

The capacitance “C” of the parallel plate capacitor is given as

C = ε_οA/d

Where
A = Area = 10 square centimeter = 6 × 10⁻⁴ meter
ε_ο = Permittivity of free space = 8.85 × 10^-12
d = distance between the parallel plate capacitor = 2mm = 2 × 10⁻³ meter
q = Charge stored in the capacitor = 8 pC = 8 × 10⁻¹²

C =  (8.85 × 10^-12 × 6 × 10⁻⁴) ⁄ 2 × 10⁻³

C = 26.55 × 10⁻¹³ F

The self-capacitance of a conductor is defined by

C = q ⁄ V

Hence the voltage across the capacitor

V = q ⁄ C = (8 × 10⁻¹²) ⁄ (26.55 × 10⁻¹³)

V = 3.013 Volts

In the given circuit the resistor of 8Ω & 8Ω are connected in parallel with each other

R_eq = (8 × 8) ⁄ (8 + 8)

R_eq = 4 Ω

Now all the three resistance i.e 4Ω, 4Ω, & 2Ω are in series therefore there equivalent resistance will be

R_eq = 4 + 4 + 2 = 10Ω

Now the value of current in the circuit

I = V/R = 40 ⁄ 10 = 4 A

To identify whether the resistance is connected in series or in parallel consider the following method

• Use one color for each continuous wire
• DO NOT cross any circuit elements
• Any element that shares the same two colors are in parallel

Now the circuit will look as shown below

As you can see from the above figure the resistance  R₁ & R₂  share two common colors i.e Green and Blue hence these two resistance are in parallel.

Similarly, the resistance R₃ & R₄  share two common colors i.e Red and Blue hence these two resistance are in parallel.

Therefore equivalent resistance for R₁ and R₂ is

R = (4 × 6) ⁄ (4 + 6) = 2.4 Ω

Similarly, the equivalent resistance for R₃ and R₄ is

R = (8 × 2) ⁄ (8 + 2) = 1.6 Ω

Now the final circuit will look like this

Since the resistance don’t share a common node hence they are connected in series

R_eq = 2.4 + 1.6 = 4Ω

Now the power delivered in the circuit is given as

P = I²R = 10² × 4

P = 400 Watt