Home
Class 12
PHYSICS
An AC source producing emf epsilon = e...

An AC source producing `emf`
`epsilon = epsilon_0 [cos(100 pi s^(-1)) t + cos (500 pi s^(-1))t]`
is connected in series with a capacitor and a resistor. The steady-state current in the circuit is found to be
`I = i_1 cos [(100 pi s^(-1) t + varphi_1] + i_2 cos [(500 pi s^(-1))t +phi_2]`.

A

`i_(1) ge i_(2)`

B

`i_(1) = i_(2)`

C

`i_(1) le i_(2)`

D

the information is insufficient to find the relation between `i_(1)` and `i_(2)`.

Text Solution

Verified by Experts

The correct Answer is:
C
`i_(1) = (in_(0))/(sqrt(R^(2) + ((1)/(100 pi C))^(2))) , i_(2) = (in_(0))/(sqrt(R^(2) + ((1)/(500 pi C))^(2)))`
Clearly `i_(1) lt i_(2)`
Promotional Banner

Topper's Solved these Questions

  • ALTERNATING CURRENT

    NARAYNA|Exercise LEVEL - VI|120 Videos

  • ALTERNATING CURRENT

    NARAYNA|Exercise LEVEL - I (H.W)|23 Videos

  • ALTERNATING CURRENT

    NARAYNA|Exercise LEVEL - IV NCERT Based Questions|15 Videos

  • ATOMIC PHYSICS

    NARAYNA|Exercise LEVEL-II (H.W)|14 Videos

Similar Questions

Explore conceptually related problems

An AC voltage e=e_(0)sin50t-e_(0)cos100pit is connected in series with a resistor and capacitor. The steady state current through circuit is found to be I=I_(0)sing(50pit+phi)+I_(0)'cos(100pit+phi_(2)) Then, the ratio of (I_(0))/(I_(0)' is

Find the effective value of current i=2+4 cos 100 pi t .

Find the effective value of current. i=2 sin 100 (pi)t + 2 cos (100 pi t + 30^(@)) .

Voltage and current in an ac circuit are given by V=5 sin (100 pi t-pi/6) and I=4 sin (100 pi t+pi/6)

int_(0)^(10 pi)cot^(-1)(cos t)dx

The time constant of an LR circuit is 40 ms. The circuit is connected at t= 0 and the steady state current is found ot be 2.0 A. Find the current at (a) t= 10 ms (b) t =20ms, (c ) t =100ms and (d) t = 1 s.

I=int_(0)^(2 pi)cos^(-1)(cos x)dx

" (i) "cos^(-1){cos(-(pi)/(4))}

NARAYNA-ALTERNATING CURRENT-LEVEL - V
  1. A lamp consumes only 50% of peak power in an a.c. circuit. What is the...

    Text Solution

    |

  2. Voltage and current for a circuit with two elements in series are expr...

    Text Solution

    |

  3. When an ac source of emfe=E(0) sin (100 t) is connected across a circu...

    Text Solution

    |

  4. The figure shows variation of R,X(L) and X(C) with frequency f in a se...

    Text Solution

    |

  5. Which of the following plots may represent the reactance of a series L...

    Text Solution

    |

  6. An inductor-coil , a capacitor and an AC source of rms voltage 24 V ar...

    Text Solution

    |

  7. A circuit consisting of a capacitor and a coil in series is connected ...

    Text Solution

    |

  8. An AC source producing emf epsilon = epsilon0 [cos(100 pi s^(-1)) t ...

    Text Solution

    |

  9. In the circuit shown in figureure the AC source gives a voltage V=20co...

    Text Solution

    |

  10. In figure i(1) = 10 e^(-2t) A, i(2) = 4 A, v(C ) = 3 e^(-2t) V Th...

    Text Solution

    |

  11. In figure i(1) = 10 e^(-2t) A, i(2) = 4 A, v(C ) = 3 e^(-2t) V Th...

    Text Solution

    |

  12. In figure i(1) = 10 e^(-2t) A, i(2) = 4 A, v(C ) = 3 e^(-2t) V Th...

    Text Solution

    |

  13. In figure i(1) = 10 e^(-2t) A, i(2) = 4 A, v(C ) = 3 e^(-2t) V Th...

    Text Solution

    |

  14. In figure i(1) = 10 e^(-2t) A, i(2) = 4 A, v(C ) = 3 e^(-2t) V Th...

    Text Solution

    |

  15. In figure i(1) = 10 e^(-2t) A, i(2) = 4 A, v(C ) = 3 e^(-2t) V Th...

    Text Solution

    |

  16. An ac generator G with an adjustable frequency of oscillation is used ...

    Text Solution

    |

  17. An ac generator G with an adjustable frequency of oscillation is used ...

    Text Solution

    |

  18. An ac generator G with an adjustable frequency of oscillation is used ...

    Text Solution

    |

  19. An ac generator G with an adjustable frequency of oscillation is used ...

    Text Solution

    |

  20. An ac generator G with an adjustable frequency of oscillation is used ...

    Text Solution

    |