Revision: Effects of Electric Current Science and Technology 1 SSC (English Medium) 10th Standard Maharashtra State Board

When a resistor is connected in an electrical circuit, heat is produced in it due to the current. This is known as the heating effect of current.

The solution through which the electricity passes is called an electrolyte.

Electric fuse is a safety device which is used in household wiring and in many appliances.

A current-carrying conductor is always associated with a magnetic field around it is called the magnetic effect of current. It was first discovered by Hans Christian Oersted in 1820.

If a current-carrying straight conductor is held in the right hand such that the thumb points in the direction of the electric current, then the fingers curled around the conductor show the direction of the magnetic field.
This is called the Right-Hand Thumb Rule.

OR

If you hold a current-carrying conductor in your right hand with the thumb pointing in the direction of the current, then the curled fingers show the direction of the magnetic field (lines of force) around the conductor.

If a conducting wire is wound in form of a cylindrical coil whose diameter is less in comparison to its length, the coil is called a solenoid.

OR

A coil of many circular turns of insulated copper wire wrapped closely in the shape of a cylinder is called a solenoid.

OR

When a copper wire with a resistive coating is wound in a chain of loops (like a spring), it is called solenoid.

If the forefinger, middle finger, and thumb of the left hand are stretched mutually perpendicular to each other, with the forefinger indicating the direction of the magnetic field, the middle finger the direction of current, then the thumb gives the direction of the force (motion) on the conductor.
This is called Fleming’s Left-Hand Rule.

OR

If the thumb, index finger, and middle finger of the left hand are stretched perpendicular to each other, and:

• The index finger points in the direction of the magnetic field,
• Middle finger in the direction of the current,
• Then the thumb gives the direction of the force (motion) on the conductor.

A device changing electrical energy into mechanical energy is known as electric motor.

lt is a device to convert electrical energy into mechanical energy. It is based on the principle that when a current-carrying coil is placed in a magnetic field, it experiences a force.

Whenever there is a change in the number of magnetic field lines linked with a conductor, an electromotive force (e.mf) is developed between the ends of the conductor which lasts as long as there is a change in the number of magnetic field lines through the conductor. This phenomenon is called the electromagnetic induction.

and

Faraday's Definition:

Electromagnetic induction is the phenomenon in which an e.m.f is induced in the coil if there is a change in the magnetic flux linked with the coil.

If the current-carrying conductor is held in the right hand such that the thumb points in the direction of the current, then the direction of the curl of the fingers will give the direction of the magnetic field.

Whenever the number of magnetic lines of force (magnetic flux) passing through a coil changes, an electric current is induced in the coil. This current is called the induced current.

If the thumb, index finger, and middle finger of the right hand are stretched perpendicular to each other, then:

• The thumb indicates the direction of motion of the conductor,
• The index finger shows the direction of the magnetic field,
• The middle finger gives the direction of the induced current.

Direct current is a non-oscillatory current that flows in one direction in a circuit, from the cell to the cell.

Rectifier: The device used to convert ac to dc is called a rectifier.

Frequency is the number of the complete cycle of variations, gone through by the ac in one second.

Alternating current is a current that changes in magnitude and direction after equal intervals of time.

lt is a device to convert mechanical energy into electrical energy. It is based on the principle of electromagnetic induction that a current is induced in a closed circuit when the magnetic field passing through it changes.

\[\vec{F}=I\vec{l}\times\vec{B}\]

It is stated that the direction of induced e.m.f. is always in such a direction that it opposes the change in magnetic flux.

e = `(d phi)/(dt)`
Consider a rectangular metal coil PQRS. Let ‘L’ be the length of the coil. It is placed in a partly magnetic field ‘B’. The direction of the magnetic field is perpendicular to the paper and into the paper. The ‘x’ part of the coil is in magnetic field at instant t. If the coil is moved towards the right with a velocity v = dx/dt with the help of an external agent, such as a hand. The magnetic flux through the coil is:

Φ = BA = BLx

∴ Φ = BLx     ...(1)

There is relative motion of a current through the coil. Let ‘i’ be current through the coil.

Three forces act on the coil.
F₁ on conductor PL ∴ F₁ = B_i x, vertically upward.
F₂ on conductor MS ∴ F₂ = B_i x, vertically downward.
F₃ on conductor SP ∴ F₃ = B_i L towards left.
F₁ & F₂ are equal and opposite and also on the same lines. They will cancel each other; F₃ is a resultant force. The external agent has to do work against this force.

∴ F₃ = −B_i l    ...(−ve sign indicates that force is opposite to dx.)
If dx is the displacement in time dt, then the work done (d_w) = F₃ dx.

∴ d_w = − B_iL dx

This power is an electrical energy ‘ei’ where ‘e’ is an induced e.m.f.

∴ e_i = `-(B_i ldx)/(dt)`

∴ e = `-(BLdx)/(dt)`

∴ e = −BLv

∴ e = `-d/dt (BLx)`

∴ e = `(-d phi)/(dt)`    ...[from eq (1)]

Lenz’s Law states that the direction of the induced electromotive force (EMF) and the resulting current in a conductor is always such that it opposes the change in magnetic flux that caused it. 

Mathematically, Lenz’s Law is expressed as:

ε = `(-d phi_B)/dt`

Where,

ε = Induced EMF

Φ_B = Magnetic flux

The negative sign indicates opposition to the change in flux.

Statement:

When the magnetic flux through a circuit is changing, an induced electromotive force (emf) is set up in the circuit whose magnitude is equal to the negative rate of change of magnetic flux. This is also known as Neumann’s Law.

Mathematical Expression:

If ΔΦ_B​ is the change in magnetic flux in a time interval Δt, then the induced emf e is given by:

e = \[-\frac{\Delta\Phi_B}{\Delta t}\]​​

In the limiting case as Δt → 0:

e = \[-\frac{d\Phi_{B}}{dt}\]​​

• If dΦ_B is in weber (Wb) and dtdtdt in seconds (s), then the emf eee will be in volts (V).
• This equation represents an independent experimental law, which cannot be derived from other experimental laws.

For a tightly-wound coil of N turns, the induced emf becomes:

e = \[-N\frac{d\Phi_B}{dt}\] or e = \[-\frac{d(N\Phi_B)}{dt}\]​

Here, NΦ_B is called the ‘number of magnetic flux linkages’ in the coil, and its unit is weber-turns.

Explanation:

Consider a magnet and a coil:

• When the north pole of a magnet is near a coil, a certain number of magnetic flux lines pass through the coil.
• If either the coil or the magnet is moved, the number of magnetic flux lines (i.e., the magnetic flux) through the coil changes.

Cases:

• Magnet moved away from the coil → Decrease in magnetic flux through the coil.
• Magnet brought closer to the coil → Increase in magnetic flux through the coil.

In both cases, an emf is induced in the coil during the motion of the magnet.

• Faster motion → Greater rate of change of flux → Higher induced emf.
• If both the magnet and coil are stationary, or both are moving in the same direction with the same velocity, there is no change in flux → No induced emf.

Special Case:

• If the coil is an open circuit (i.e., infinite resistance), emf is still induced, but no current flows.
• This shows that it is the change in magnetic flux that induces emf, not current.

Conclusion:

Neumann’s Law establishes that a changing magnetic flux through a circuit induces an emf, and the induced emf is proportional to the rate of change of flux, with a negative sign indicating the direction (as per Lenz’s law).

Limitations:

• The law applies to changing magnetic flux; it does not induce emf if the magnetic flux remains constant.
• No emf is induced if the coil and magnet move together at the same velocity or remain stationary.
• In open circuits, emf is induced, but no current is generated.

Statement:

The direction of the induced emf, or the induced current, in any circuit is such as to oppose the cause that produces it. This law is known as Lenz’s Law.

Explanation / Proof:

• When the north pole of a magnet is moved towards the coil, an induced current flows in the coil in such a direction that the near (left) face of the coil behaves like a north pole.
• Due to the repulsion between the like poles, the motion of the magnet towards the coil is opposed.
• When the north pole of the magnet is moved away from the coil, the induced current flows in such a direction that the near face of the coil becomes a south pole.
• The attraction between opposite poles then opposes the motion of the magnet away from the coil.

In both cases, the induced current opposes the magnet's motion, which is the cause of the current. Therefore, work has to be done to move the magnet, and this mechanical work appears as electrical energy in the coil.

Direction of Induced Current (Fleming’s Right-Hand Rule):

• Stretch the right-hand thumb, forefinger, and middle finger so that they are mutually perpendicular.
• The forefinger points in the direction of the magnetic field.
• The thumb points in the direction of motion of the conductor.
• The middle finger then gives the direction of the induced current.

Conclusion:

Lenz’s Law shows that the induced current always acts in such a direction as to oppose the cause that produces it. This ensures that mechanical energy is converted into electrical energy, and no energy is produced without work being done.

Limitations / Note:

• If the induced current were in a direction that did not oppose the motion of the magnet, electrical energy would be obtained continuously without doing any work, which is impossible.
• Hence, Lenz’s Law is consistent with the principle of conservation of energy.

• Electric current creates a magnetic field, shown by compass needle deflection.
• Oersted discovered the link between electricity and magnetism in 1820.
• Reversing current changes the direction of the magnetic field.
• Iron filings form circular patterns, showing magnetic field lines around the wire.
• Magnetic field strength increases with current and decreases with distance.

• A current-carrying conductor placed in a magnetic field experiences a force when the direction of current is not parallel to the magnetic field.
• The direction of force reverses when the direction of current or the direction of magnetic field is reversed, and no force acts when current flows parallel to the magnetic field.

• Electromagnetic induction can be used to generate a large current by rotating a coil in a magnetic field, converting mechanical energy into electrical energy.
• In an AC generator, a coil rotates between magnetic poles, and the induced current reverses direction every half-rotation, producing alternating current (AC).
• Carbon brushes and conducting rings connect the rotating coil to the external circuit; the current direction in the circuit reverses after each half-turn.
• Using a multi-turn coil significantly increases the magnitude of the generated current.
• A DC generator uses a split ring instead of two separate rings to maintain unidirectional current in the external circuit.