  Difficult Conceptual Numericals

## Electromagnetic Induction

- Solve the toughest problems
1
Current induced in a circuit due to magnetic flux.
Find the current (as a function of time t) in the circuit consisting of a source of constant emf E and a choke coil of inductance L connected in series.
A closed circuit consists of a source of constant emf and a choke coil of inductance connected in series. The active resistance of the whole circuit is equal to . At the moment the choke coil inductance was decreased abruptly times. Find the current in the circuit as a function of time .
Instruction. During a stepwise change of inductance the total magnetic flux (flux linkage) remains constant.
2

The magnetic flux through a stationary loop with resistance R varies during the interval of time T as ./ The heat generated during this time neglecting the inductance of the loop will be :

A
B
C
D
3
Problem on faraday law and Lenz's law.
Faraday's Laws of Electromagnetic Induction consists of two laws. The first law describes the induction of EMF in a conductor and the second law quantifies the EMF produced in the conductor. According to Lenz's Law, if an induced current flows in a coil due to electromagnetic induction, its direction is always such that it will oppose the change which produced it.
Three resistance of magnitude each are connected in the form of an equilateral triangle of side . The combination is placed in a magnetic field
perpendicular to the plane. The induced current in the circuit is given by:
A
B
C
D
4
A system (e.g. circuit) is in the steady state when the current at each point in the circuit is constant (does not change with time). In many practical circuits, the steady state is achieved in a short time.
A solenoid of inductance and resistance is connected in parallel to a resistance and a battery of emf . Initially if the switch is closed for a long time and at , then the :
A
current through solenoid at any time , after opening the switch is
B
induced emf across solenoid at time is
C
amount of heat generated in solenoid is
D
potential difference across solenoid at is
5
Mutual inductance
Mutual Inductance is the interaction of one coils magnetic field on another coil as it induces a voltage in the adjacent coil.
Find the mutual inductance between the circular coil of radius and the loop of radius as  shown in figure when the slider on the rheostat is moved. The total resistance of rheostat is R and the distance between the center of two coils is x.
6
Energy stored in an inductor due to magnetic field.
The energy stored in a magnetic field is equal to the work needed to produce a current through the inductor having self inductance (L).
A solenoid of henry  inductance and ohm resistance is connected to a volt battery. In how much time the magnetic energy will be reaches to th of the maximum value?
A
B
C
D
7
EMF And Current In AC Generator
AC generators work on the principle of Faraday's law of electromagnetic induction which states that electromotive force -EMF or voltage - is generated in a current-carrying conductor that cuts a uniform magnetic field. Let's solve a problem to understand it properly.
An ac generator has emf  , with    and  . It is connected to a    inductor. (a) What is the maximum value of the current? (b) When the current is a maximum, what is the emf of the generator? (c) When the emf of the generator is  and increasing in magnitude, what is the current?