NEET Practice Questions (MCQs) with Answers & Solutions

The passage states, 'The formulae we have derived earlier for series and parallel combinations of resistors are not always sufficient to determine all the currents and potential differences in the circuit. Two rules, called Kirchhoff’s rules, are very useful for analysis of electric circuits.'

While not explicitly stated as a formula, the example 3.6 demonstrates that applying the loop rule to remaining closed loops 'does not provide any additional independent equation' once a sufficient number of independent equations has been formed to solve for the unknowns. The number of independent equations from the loop rule is generally equal to the number of unknown currents that cannot be determined by the junction rule.

The junction rule states: 'At any junction, the sum of the currents entering the junction is equal to the sum of currents leaving the junction.' Therefore, if $I_1$ and $I_2$ enter and $I_3$ leaves, then $I_1 + I_2 = I_3$.

The context mentions, 'If, while labelling the current I through the cell one goes from P to N, then of course V = e + I r (3.60)'. This implies that when current flows from P to N through the cell, the terminal voltage is $e+Ir$.

The text states: 'Given a circuit, we start by labelling currents in each resistor by a symbol, say I, and a directed arrow to indicate that a current I flows along the resistor in the direction indicated.'

Lenz's law is a consequence of the law of conservation of energy. The induced current's direction is such that it opposes the change in magnetic flux, thus requiring external work to maintain the change, which is then dissipated as heat. If it aided the change, it would generate energy spontaneously, violating conservation of energy. (Refer to NCERT text: 'This violates the law of conservation of energy and hence can not happen.')

As the North pole approaches, the magnetic flux increases. To oppose this increase, the induced current creates a magnetic field with its North pole facing the approaching magnet, resulting in a repulsive force. By the right-hand thumb rule, this corresponds to a counter-clockwise current as observed from the side of the magnet. (Refer to NCERT text: 'As the North-pole of the bar magnet moves towards the coil, the magnetic flux through the coil increases. Hence current is induced in the coil in such a direction that it opposes the increase in flux. This is possible only if the current in the coil is in a counter-clockwise direction with respect to an observer situated on the side of the magnet.')

When the North pole of the magnet is withdrawn, the magnetic flux through the coil decreases. To oppose this decrease, the induced current creates a magnetic field with a South pole facing the receding North pole of the magnet, resulting in an attractive force that tries to prevent the magnet from being withdrawn. (Refer to NCERT text: 'Similarly, if the North-pole of the magnet is being withdrawn from the coil, the magnetic flux through the coil will decrease. To counter this decrease in magnetic flux, the induced current in the coil flows in clockwise direction and its South-pole faces the receding North-pole of the bar magnet. This would result in an attractive force which opposes the motion of the magnet and the corresponding decrease in flux.')

If the magnetic field is directed away from the reader and the flux is increasing, the induced current must create a magnetic field directed towards the reader (opposite to the original increasing field) to oppose this increase. By the right-hand thumb rule, a counter-clockwise current produces a magnetic field directed towards the reader. (Example 6.4 (i) in NCERT text illustrates this principle in reverse, where flux increases, so current is clockwise to oppose, by creating field towards reader. If field is into the page and increasing, the induced current would aim to create a field coming out of the page, which is counter-clockwise.) Let's re-evaluate: 'The magnetic flux through the rectangular loop abcd increases, due to the motion of the loop into the region of magnetic field, The induced current must flow along the path bcdab so that it opposes the increasing flux.' For a field 'away from the reader' (into the page) that is increasing, the induced current must create a field 'towards the reader' (out of the page). This is achieved by a counter-clockwise current.

If the induced current supported the change, the system would continuously accelerate without external energy input, creating a perpetual motion machine. This violates the law of conservation of energy. (Refer to NCERT text: 'A gentle push on the magnet will initiate the process and its velocity and kinetic energy will continuously increase without expending any energy. If this can happen, one could construct a perpetual-motion machine by a suitable arrangement. This violates the law of conservation of energy and hence can not happen.')