Home
Class 12
PHYSICS
A charged capacitor of capacitance C is ...

A charged capacitor of capacitance C is discharged through a resistance R. A radioactive sample decays with an average-life `tau`.Find the value of R for which the ratio of the electrostatic field energy stored in the capacitor to the activity of the radioactive sample remains constant in time.

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Promotional Banner

Topper's Solved these Questions

  • THE NUCLEOUS

    HC VERMA|Exercise Objective 2|10 Videos

  • SPEED OF LIGHT

    HC VERMA|Exercise Exercises|3 Videos

  • THE SPECIAL THEORY OF RELATIVITY

    HC VERMA|Exercise Exercises|27 Videos

Similar Questions

Explore conceptually related problems

A radioactive sample decays with an average life of 20 ms . A capacitor of capacitance 100 muF is charged to some potential and then the plates are connected through a resistance R . What should be the value of R so that the ratio of the charge on the capacitor to the activity of the radioactive sample remains constant in time?

A capacitor has some dielectric between its plates and the capacitor is connected to a DC source. The battery is now disconnected and then the dielectric is removed. State whether the capacitance, the energy stored in it, electric field, charge stored and the voltage will increase, decrease or remain constant.

The series combination of R (Omega) and capacitor C(F) is connected to an A.C. source of V volts and angular frequency omega . If the angular frequency is reduced to omega/3 , the current is found to be reduced to one-half without changing the value of the voltage. Determine the ratio of the capacitive reactance and the resistance.

An electromagnetic wave can be represented by E = A sin (kx- omega t + phi) , where E is electric field associated with wave, According this equation, for any value of x, E remains sinusoidal for -oolt t lt oo . Obviously this corresponds to an idealised situation because radiation from ordinary sources consists of finite size wavetrains. In general, electric field remains sinusoidal only for times of order tau_(c) ' which is called coherence time. In simpler language it means that for times of order tau_(c)' a wave will have a definite phase. The finite value of coherence time could be due to many factors, for example if radiating atom undergoes collision with another atom then wave train undergoes an abrupt phase change or due to the fact that an atom responsible for emitting radiation has a finite life time in the energy level from which it drops to lower energy level, while radiating. Concept of coherence time can be easily understood using young's double slit experiment. Let interference patten is observed around point P at time t , due to superposition of waves emanting from S_(1) and S_(2) at times t =(r_(1))/(c) and (r_(2))/(c) respectively, where r_(1) and r_(2) are the distances S_(1) P & S_(2)P . Obviously if (r_(2)-r_(1))/(c) lt lt tau_(e),{"where" " "c = 3xx10^(8)m//s} then, wavetrain arriving at point P from S_(1) & S_(2) will have a definite phase relationship and an interference pattern of good contranst will be obtained. If coherence time is of order 10^(-10) second and screen is placed at a very large distance from slits in the given figure, then:-

An electromagnetic wave can be represented by E = A sin (kx- omega t + phi) , where E is electric field associated with wave, According this equation, for any value of x, E remains sinusoidal for -oolt t lt oo . Obviously this corresponds to an idealised situation because radiation from ordinary sources consists of finite size wavetrains. In general, electric field remains sinusoidal only for times of order tau_(c) ' which is called coherence time. In simpler language it means that for times of order tau_(c)' a wave will have a definite phase. The finite value of coherence time could be due to many factors, for example if radiating atom undergoes collision with another atom then wave train undergoes an abrupt phase change or due to the fact that an atom responsible for emitting radiation has a finite life time in the energy level from which it drops to lower energy level, while radiating. Concept of coherence time can be easily understood using young's double slit experiment. Let interference patten is observed around point P at time t , due to superposition of waves emanting from S_(1) and S_(2) at times t =(r_(1))/(c) and (r_(2))/(c) respectively, where r_(1) and r_(2) are the distances S_(1) P & S_(2)P . Obviously if (r_(2)-r_(1))/(c) lt lt tau_(e),{"where" " "c = 3xx10^(8)m//s} then, wavetrain arriving at point P from S_(1) & S_(2) will have a definite phase relationship and an interference pattern of good contranst will be obtained. If coherence time is of order 10^(-10) second and screen is placed at a very large distance from slits in the given figure, then:-

A radioactive sample consists of two distinct species having equal number of atoms initially. The mean life of one species is tau and that of the other is 5 tau . The decay products in both cases are stable. A plot is made of the total number of radioactive nuclei as a function of time. Which of the following figure best represents the form of this plot? (a), (b), (c), (d)

A parallel plate capacitor with circular plates of radius 1 m has a capacitance of 1 nF. At t = 0, it is connected for charging in series with a resistor R = 1 M Onega across a 2V battery. Calculate the magnetic field at a point P, halfway between the centre and the periphery of the plates, after t=10^(-3)s . (The charge on the capacitor at time t is q (t) = CV [1 - exp (-t//tau) ], where the time constant tau is equal to CR.)

A cylindrical capacitor with external radius R, internal radius R-d(dltltR ) , length l and mass M hangs on an insulating cord in a region where there is a homogenous, vertical magnetic field of strength B. It can rotate freely as a whole around its vertical axis, but is constrained, so that it can not move horizontally. The capacitor is charged and there is a voltage difference If without being mechaically disturbed, the capacitor is discharged through an internal radial wire then find maximum angular velocity of capacitor

A parallel plate capacitor with circular plates of radius 0.8 m has a capacitance of 1 nF. At t = 0, it is connected for charging in series with a resistor R = 1 M Omega across a 4V battery. Calculate the magnetic field at a point P, halfway between the centre and the perpendicular of the plates after t=10^(-3)s . (The charge on the capacitor at time t is q (t) = CV [1 - exp (-t//tau) ], where the time constant tau is equal to CR.)

Answer carefully: (a) Two large conducting spheres carrying charges Q_(1) and Q_(2) are brought close to each other. Is the magnitude of electrostatic force between them exactly given by Q_(1),Q_(2)//4pi epsilon_(0)r^(2) , where r is the distance between their centres? (b) If Coulomb’s law involved 1//r^(3) dependence (instead of would Gauss’s law be still true ? (c) A small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point? (d) What is the work done by the field of a nucleus in a complete circular orbit of the electron? What if the orbit is elliptical? (e) We know that electric field is discontinuous across the surface of a charged conductor. Is electric potential also discontinuous there? (f) What meaning would you give to the capacitance of a single conductor? (g) Guess a possible reason why water has a much greater dielectric constant (= 80) than say, mica (= 6).

HC VERMA-THE NUCLEOUS-Exercises
  1. Natural water contains a small amount of tritium (1^3H). This isotope ...

    Text Solution

    |

  2. The count rate of nuclear radiation coming from a radioactive sample c...

    Text Solution

    |

  3. The half-life of K-40 is 1.30×10^ 9 year. A sample of 1.0 g of pure ...

    Text Solution

    |

  4. 80^197Hg decay to 79^197Au through electron capture with a decay const...

    Text Solution

    |

  5. A radioactive isotope is being produced at a constant rate dN//dt=R in...

    Text Solution

    |

  6. Consider the situation of the previous problem.suppose the production ...

    Text Solution

    |

  7. In an agriculture experiment, a solution containing 1 mole of a radioa...

    Text Solution

    |

  8. A vessel of vloume 125 cm^3 contains tritium (^3H,t(1//2)=12.3 y) at 5...

    Text Solution

    |

  9. 83^212Bi can disintegrate either by emitting an alpha -particle or by ...

    Text Solution

    |

  10. A sample contains a mixture of ^110Ag and ^108Ag isotopes each having ...

    Text Solution

    |

  11. A human body excretes (removes by waste discharge, sweating, etc,) cer...

    Text Solution

    |

  12. A charged capacitor of capacitance C is discharged through a resistanc...

    Text Solution

    |

  13. Radioactive isotopes are produced in a nuclear physics experiment at a...

    Text Solution

    |

  14. Calculate the energy released by 1 g of natural uranium assuming 200 M...

    Text Solution

    |

  15. A uranium rector develops thermal energy at a rate of 300 MW. Calculat...

    Text Solution

    |

  16. A town has a population of 1 million. The average electric power neede...

    Text Solution

    |

  17. Calculate the Q-values of the following fusion reactions: (a)1^2H+1^2H...

    Text Solution

    |

  18. Consider the fusion in helium plasma. Find the temperature at which th...

    Text Solution

    |

  19. Calculate the Q-values of the fusion reaction ^4(He)+^4He=^8(Be). I...

    Text Solution

    |

  20. Calculate the energy that can be obtained from 1 kg of water through t...

    Text Solution

    |