GAT Test - 8

Concept:

• When a bar magnet is cut into equal parts, each part becomes a bar magnet.
• Bar magnet:
  • ​A bar magnet is a rectangular piece of an object, made up of iron, steel, or any other ferromagnetic substance or ferromagnetic composite, that shows permanent magnetic properties.
  • It has a north pole and a south pole at two ends. Even if you break a bar magnet from the middle, both the pieces will still have a north pole and a south pole, no matter how many pieces you break it in.
  • Its magnetic force of it is the strongest at the poles.
  • A bar magnet will attract all ferromagnetic materials such as iron, nickel, and cobalt.

• Pole strength:
  • ​It is defined as the strength of a magnetic pole to attract magnetic materials toward itself.
  • Pole strength is a scalar quantity.

Explanation:

• When a bar magnet is cut into two equal halves perpendicular to its length.
• Then, the pole strength of each piece is the same as the pole strength of the original bar magnet.

CONCEPT:

The force between two parallel currents:

• We know that there exists a magnetic field due to a conductor carrying a current.
• And an external magnetic field exerts a force on a current-carrying conductor.
• Therefore we can say that when two current-carrying conductors placed nearby each other will exert (magnetic) forces on each other.
• In the period 1820-25, Ampere studied the nature of this magnetic force and its dependence on the magnitude of the current, on the shape and size of the conductors, as well as, the distances between the conductors.
• Let two long parallel conductors a and b separated by a distance d and carrying (parallel) currents Ia and Ib respectively.
• The magnitude of the magnetic field intensity due to wire a, on the wire b is,

• The magnitude of the magnetic field intensity due to wire b, on the wire a is,

• The conductors 'a' and ‘b’ carrying a current Ia and Ib respectively will experience sideway forces due to magnetic field Bb and Ba respectively

EXPLANATION:

• If two current-carrying long wires A and B are placed parallel to each other and separated by a distance d. Then the force F on the segment L of the wires is given as,

• When the current flows in the same direction in the two parallel wires then both wires attract each other and if the current flows in the opposite direction in the two parallel wires then both wires repel each other.

EXPLANATION:

→A solenoid consists of a helical winding of wire on a cylinder, usually circular in cross-section.

There can be hundreds or thousands of closely spaced turns, each of which can be regarded as a circular loop.

→Magnetic field due to solenoid B = μ₀nl

μ0 = Permeability of free space

n = no. of windings per unit length

I = current.

→The direction of the field inside the solenoid is parallel to the axis, obtained by the right-hand thumb rule.

The direction of the field is shown in the figure.

→If a charged particle (q) is projected with uniform velocity along the axis of the solenoid then the force on the electron

∴ F = qvB sin0 or qvB sin180

∴ F = 0

Hence, the electron will continue to move with uniform velocity.

So, the correct answer is option (4).

Explanation:

Fleming’s Left-Hand Rule:

• A current-carrying conductor when placed in a magnetic field will experience a force by this conductor.
• The direction of force acting on this conductor will depend upon the direction of the magnetic field and the current flowing through the conductor.
• Fleming’s Left-Hand Rule can be used to find the direction of this current flow.

So, statement A is correct.

The direction of the magnetic field at a point P due to a long, straight wire can be found by a slight variation in the right- hand thumb rule.

• If we stretch the thumb of the right hand along the long current and curl our fingers to pass through the point P, the direction of the fingers at P gives the direction of the magnetic field there.
• A tangent to a magnetic field line gives the direction of magnetic field existing at that point.

So, statement B is correct.

The frequency of Alternating Current in India is 50 Hz. Since the current reverses every half revolution, current in India reverses every 1/100th or 0.01th of a second.

So, statement C is incorrect.

​DC and AC transmission - Electric power can be transmitted either by AC transmission system (i.e., the voltage and current are alternating) or DC transmission system (i.e., the voltage and current are direct or unidirectional). Each transmission system has its own advantages and disadvantages.

• The construction of AC transmission lines is more complicated than the DC transmission lines.
• AC transmission lines require more conductor material than the DC transmission lines as three wires are required for AC transmission.
• The effective resistance of the AC transmission line is higher than DC transmission line. It is because the skin effect takes place in AC transmission line.
• An AC transmission line has line capacitance. Therefore, there is a continuous power loss in the AC transmission line due to line charging current even when the line is open.
• There is no capacitance in the DC transmission. Therefore, there is no power loss due to the charging current.
• For the same sending end voltage and load conditions, the voltage drop in the DC transmission line is less than the AC transmission line. It is because of the absence of inductance in DC transmission line.
• So, we can say that advantage of DC over AC is that the electric power can be transmitted to distant places without appreciable loss of energy.

So, statement D is correct.

CONCEPT:

• As the current-carrying conductor experiences a force when placed in a magnetic field, each side of a current-carrying circular coil experiences a force in a magnetic field.
• In the present section, we shall see in what way the circular loop carrying current is influenced by a magnetic field.

• Consider a circular coil of length l and breadth b carrying a current I placed in a uniform magnetic field B.
• θ, be the angle between the plane of the circular coil and the magnetic field.

 Force acting on the circular loop:

F = I L B sinθ, where F is force, I = current, L = distance from the axis, B = strength of the magnetic field, θ = angle between the plane of the circular coil and the magnetic field.

• Acting on the upper and lower sides are equal and opposite along the same line of action, they cancel each other.
• As the force acting on the sides QR and SP are equal and opposite along different lines of action they constitute a couple.

So, the torque acting on the loop is,

T = force × arm of the couple

T = B I L × b Sinθ = B I A Sinθ

T = B I A Sinθ

EXPLANATION:

• The torque acting on a circular current-carrying loop placed in a uniform magnetic field depends upon
  • area of the loop
  • value of current
  • magnetic field
• The torque acting on the circular loop is

T = B I A Sinθ.

So option 2 is correct.

Concept:

•  A material or object that produces a magnetic field is called magnetic material.
• In physics, there are three types of magnetic materials: Paramagnetic materials, Diamagnetic materials, and ferromagnetic materials.​​

Ferromagnetic material:

• ​Ferromagnetic materials are those materials that exhibit a spontaneous net magnetization at the atomic level, even in the absence of an external magnetic field.
• For example Iron, Cobalt, Nickel.

Magnetization:

• This is also termed magnetic polarization.
• A vector quantity that measures the density of permanent or induced dipole moment in a given magnetic material.
•  It is defined as the net magnetic moment for that material per unit volume.
• Formula, magnetization, M = m_n/V, where, m_n = net magnetic moment, V = volume
• When a ferromagnetic material inserts inside the solenoid, the magnetic field increases.

Explanation:

• When an iron rod or other ferromagnetic material is placed within the solenoid.
• The ferromagnetic material becomes magnetized, thus creating an electromagnet.
• The presence of the ferromagnetic rod within the solenoid greatly increases the strength of the magnetic field.

Additional Information

Solenoid:

• The solenoid is a type of electromagnet, the purpose of which is to generate a controlled magnetic field through a coil wound into a tightly packed helix.
• The magnetic field is formed around the coil when an electric current passes through it and draws the plunger in.

• The magnetic field at the center of the solenoid, B = μ₀ nI, where, n = number of turns per unit length, I = current 

Explanation:

Magnetic field and magnetic lines of force: It is the space around a magnetic pole or magnet or current-carrying wire within which its magnetic effect can be experienced is defined as a magnetic field.

• The magnetic field can be represented with the help of a set of lines or curves called magnetic lines of force or magnetic field lines.

Properties of magnetic field line:

1. The magnetic field line is directed from the north pole to the south pole outside and south to the north inside the magnet.
2. Magnetic field lines are closed and continuous.
3. Magnetic field lines are more crowded near poles which shows that the strength of the magnetic field is maximum at its poles.
4. Magnetic field lines never intersect with each other.

​The reason being is that if two field lines intersect each other, then there will be two directions of the magnetic field, which is not possible.

Mistake Points
In the question, it is given that, Magnetic line of forces always starts from the north pole and ends at the south pole of the magnet. But it is not mentioned that, at the outer side or inner side. therefore, technically the given sentence is Incorrect.

Properties of magnetic field line:

• The magnetic field line is directed from the north pole to the south pole outside and south to the north inside the magnet.

Concept:

Resistance:

• It is a measure of the opposition to current flow in an electrical circuit.
• Resistance is measured in ohms, symbolized by the Greek letter omega (Ω).

In parallel combination of resistors: 

• Resistors are in parallel if their terminals are connected to the same two nodes.
• The equivalent overall resistance is smaller than the smallest parallel resistor.

Additional Information

​In series combination of resistors:

• ​Two or more resistors are said to be connected in series when the same amount of current flows through all the resistors.
• In such circuits, the voltage across each resistor is different. In a series connection, if any resistor is broken or a fault occurs, then the entire circuit is turned off.

Explanation:

→ For a Galvanometer increasing the number of turns leads to an increase in current sensitivity but along with that resistance also increases.

Hence reason is true.

→ Increasing the value of current sensitivity does not mean that voltage sensitivity will also increase because Voltage sensitivity is given as:

→ Both I_G and R if changed by different amounts may increase or decrease the voltage sensitivity.

Hence assertion is true.

Hence, the correct option is (1)

Concept:

Power dissipation:

• It is the process of loss of power in the form of heat due to primary action.
• It is a naturally occurring process.
• All the resistors that are part of the circuit and have a voltage drop across them will dissipate power.
• The electrical power gets converted to heat energy, and therefore all the resistors will have a power rating.
• The power rating is the maximum power that can be dissipated from a resistor without burning out.
• Across the resistors, the power dissipation is, P = VI
• Or, P = I² R, where R = resistance, I = current

Calculation:

The current I through a resistor is increased by 100%.

Power is calculated as the product of voltage and current, which can further lead to, P = I²R

When the current through the resistor is increased by 100%, the new value of the circuit's current, indicated by I′, can be calculated as,

I' = I + 100% of I

I' =  2I

Then the power dissipated across the resistor can be calculated as,

P' = I'² R

 P' = 4I²R

P' = 4P

When the current is increased by 100%, the power change is calculated as follows:

Percentage, 3 × 100 = 300%