For Jee mains and and AIPMT

Many a times it is asked that when a north (or)south pole of a magnet is placed on a horizontal board, where could be the neutral point I.e. the point where horizontal component of the earth,s magnetic field is cancelled by the horizontal magnetic field component of the other magnetic source . The following two figures may help in getting the answer. The first fig shows how the magnetic field lines surround a magnet. This clearly hints that when this magnet is placed on a horizontal board with north pole on the board, the horizontal component of the filed lines looks like those , drawn in the fig 2.

Maths For JEE mains... Vector 18 feb

LC Oscillations

LC Oscillations refers to a situation

• where a circuit contains capacitor and inductor only and charge on the capacitor and current in the circuit, keeps on oscillating harmonically with time.
• where if charge on the capacitor decreases ( in magnitude) with time then current in the circuit increases with time.
• where sum of electrostatic energy in the capacitor and magnetic energy in the inductor, remains constant.

The oscillation frequency of current or charge, depends on the product of the self inductance and capacitanceC in the circuit. If this product is more then the frequency of the oscillation will be lesser.

If the charge and current oscillates with the angular frequency w then the w is equal to the square root of the inverse of the term LC for the circuit. So if both L and C are doubled then the angular frequency will be halved.

The variation of the charge or current with time will be similar to the variation of the position and velocity respectively of a block performing shm while being connected to one end of a spring . Is

• If initially charge on the capacitor is maximum, then after time t , it will be proportional to cosine of wt and current will be proportional to sine of wt.
• If initially current is maximum, then after time t current will be proportional to cosine of wt and the charge will be proportional to sine of wt.

Following are the questions relating to a circuit, which contains only L and C :

1-In the circuit, at time t =0, current is found to be zero and after 2 microseconds, the current grows to it's maximum value. What is the value the term LC for this circuit?

2-In the circuit, at time t =0, current is found to be zero and after 2 microseconds, the current grows to it's maximum value. What is lest value of the time t , when energy stored in the inductor attains half of it's maximum value?

3-In the circuit, initially current is maximum and equals to 10 A. What will be the current when energy stored in the capacitor is three fourth of the total electromagnetic energy of the circuit?

4-In the circuit, initially energy stored in the capacitor and the inductor are same. If this happens again happens 4 microseconds later and never before, then what is the time period of oscillation of the current ?

5-Second derivative of charge with respect to time equals negative of 400 multiplied by the charge. What is the value of the expression LC for the circuit?

Viresh

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Viresh Singh
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Viresh

Motional EMF

The following is description of a problem where loop is pulled in a magnetic region cutting the magnetic field lines. This article gives summary of the result relating to the variation of induced emf with time/ position

RC. Circuit dc source..

Gzb 01 Feb 14

1-In context of transistors, the coefficient hfe is same as beta .

2-In oscillators transistor operates in active mode as it works as amplifier there.

3-(a)In case of photoelectric experiment , if the power of the source is doubled and frequency of the light is also doubled, then saturation photoelectric current still remains unchanged.
3(b)In case of photoelectric experiment, if the source of light is a point source and it is moved to twice distance from the photoelectric plate, the saturation photoelectric current will decrease to one fourth but the stopping potential will remain same

4-In a series RLC ac circuit , quality factor

• decreases if resistance is increased
• decreases if the capacitance is increased
• increases if the self inductance is increased.

5-In series RLC ac circuit, the power factor

• Increases if the resistance increases
• may increase or decrease on increasing the self inductance depending on the value of the source frequency in comparison to the resonance frequency.

6-In hydrogen like atom, if the electron moves to higher energy level, it's kinetic energy decreases by same amount as the total energy increases.

7-In hydrogen like atom, deBroglie wavelength of the electron will be directly proportional to the principal quantum number of the orbit in which the electron is rotating.

8-Two magnets placed at large distance x from one another, exert force and torque on each other.
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9- In the above arrangements, in the first fig, the two magnets repel each other and apply clockwise torque on each other. In the second fig, the two magnets attract each other but will not exert torque. Note that the two magnets exert force on each other which vary as Fourth power of the inverse of their separation.

10-When light wave is reflected from an optically denser medium, it suffers phase change of 180 degree.

11- When a transparent sheet is pasted in front of any one slit in YDSE, then fringes move towards that slit , in this case fringe width remains unchanged but the order of a fringe at given location on the screen , changes by (n-1)t/ wavelength.

12-In amplifies with transistor operating in CE mode, output potential differs in phase by 180 degree with respect to input .

Viresh