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Electromagnetic Induction Test - 5

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Electromagnetic Induction Test - 5
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Weekly Quiz Competition
  • Question 1
    1 / -0
    What are the the dimensions of , where L, R, C and V have their usual meanings?
    Solution
    emf = V = L dI/dt
    L = V dt/dI
    RC is time constant. Its dimension are equal to time.
    So, dimensions of = Vdt/dl
    RCV = 1/A = M0L0A-1T0
  • Question 2
    1 / -0
    In an LCR series circuit, the potential difference between the terminals of the inductance is 60 V, that between the terminals of the capacitor is 30 V and that across the resistance is 40 V. Then, the supply voltage will be
    Solution
  • Question 3
    1 / -0
    In an oscillating LC circuit, the maximum charge on the capacitor is Q. The charge on the capacitor, when energy is stored equally between the electric and magnetic fields, is
    Solution
    If energy is stored equally in electric and magnetic fields, then energy in electric field will be half of the maximum value, which occurs when the charge on the capacitor is maximum.
    Energy in capacitor =

    Q' =
  • Question 4
    1 / -0
    A coil takes a current of 2 A and 200 W power from an alternating current source of 220 V, 50 Hz. What is the inductance of the coil?
    Solution



    = = 50

    Z = =

    Z = V/I = 220/2 = 110 ohm

    = 12100 - 2500 = 9600


    = 98 ohm

    L = = = = 0.312 H
  • Question 5
    1 / -0
    A circular metal plate of radius 'R' is rotating with a uniform angular velocity 'ω' with its plane perpendicular to a uniform magnetic field B. Then, emf developed between the centre and the rim of the plate is
    Solution

    The change will accumulate on the rim due to half effect until their fields are balanced by the magnetic field's force at a radius r.
    Let the field be E.
    dq E = Br dq (q)
    E = B r
    Now, total emf =
    emf =
  • Question 6
    1 / -0
    In an LR circuit, the reactance of the given inductor L is 40 , and the value of R is 30 . If in the circuit, an alternating emf of 200 V at 50 cycles/s is connected, the impedance of the circuit and the current will be
    Solution
    Z = (R2 + XL2)1/2
    Z = {(40)2 + (30)2}1/2 = 50 ohms
    I = V/Z = 200/50 = 4 A
  • Question 7
    1 / -0
    A short solenoid of length 4 cm, radius 2 cm and 100 turns is placed inside and on the axis of a long solenoid of length 80 cm and 1500 turns. A current of 3 A flows through the short solenoid. The mutual inductance of the two solenoids is
    Solution
  • Question 8
    1 / -0
    In a coil, if current changes from 10 A to 2 A in 0.1 s, the induced emf is 3.28 V. What is the self-inductance of the coil?
    Solution
  • Question 9
    1 / -0
    What is the capacitance of a capacitor whose reactance for AC frequency of 400 Hz is 25?
    Solution


  • Question 10
    1 / -0
    A 100 V AC source of frequency 500 Hz is connected to an LCR circuit with L = 8.1 mH, C = 12.5 µF and R = 10 (all are connected in series as shown in the figure). What is the quality factor of the circuit?

    Solution
    The Q-factor of series resonant circuit is defined as the ratio of the voltage developed across the inductance or capacitance at resonance to the impressed voltage, which is the voltage applied across R.

  • Question 11
    1 / -0
    In an AC circuit, the voltage applied is E = E0 sin ωt. The resulting current in the circuit is I = I0 sin . The power consumption in the circuit is given by
    Solution
  • Question 12
    1 / -0
    If an alternating voltage is represented as E = 141 sin (628t), then what are the R.M.S. values of the voltage and the frequency?
    Solution
  • Question 13
    1 / -0
    If current of 30 A flowing in a primary coil is made zero in 0.1 sec, the emf induced in a secondary coil is 1.5 V. What is the mutual inductance between the coils?
    Solution
    E = L
    1.5 = L ×
    L = 0.005 H
  • Question 14
    1 / -0
    The primary and secondary coils of a transformer have 50 and 1500 turns respectively. If the magnetic flux φ linked with the primary coil is given by φ = φ0 + 4t (where φ is in weber, t (time) is in seconds and φ0 is a constant), the output voltage across the secondary coil is
    Solution
    Flux linked with the primary coil is

    Voltage across the primary coil,


    From the transformer ratio,

    Output voltage,
  • Question 15
    1 / -0
    A transformer has an efficiency of 80%. It is connected to a power input of 5 kW at 200 V. If the secondary voltage is 250 V, what are the primary and secondary currents respectively?
    Solution
  • Question 16
    1 / -0
    A coil of resistance 100 and inductance 100 H is connected in series with 100 pF capacitor. What is the resonant frequency of the circuit?
    Solution
    Vr =
    =
    =
    = × 106
    = 1.59 × 106
  • Question 17
    1 / -0
    The following series resonant LCR circuit has a quality factor (Q-factor) of 0.4 and a bandwidth of 1.3 kHz. What is the value of inductance?

    Solution
  • Question 18
    1 / -0
    The magnetic flux linked with a coil at any instant 't' given by another emf induced in the coil at t = 2s is
    Solution
  • Question 19
    1 / -0
    The value of mean induced e.m.f. in a coil is 8 volt. If the value of current in it varies from 2 amp to 4 amp in 0.05 second, what is self inductance of the coil?
    Solution
    EMF = L
    8 = L x
    = L
    L = 0.20
  • Question 20
    1 / -0
    In an LCR circuit, the capacitance is changed from C to 4C. For the same resonant frequency, what should be the inductance?
    Solution
    In an LCR circuit, resonance frequency is given by



    For same resonant frequency, LC should be constant.
  • Question 21
    1 / -0
    A coil of 40 H inductance is connected in series with a resistance of 8 and this combination is connected to the terminals of a 2 V battery. The inductive time constant (in seconds) of the circuit is
    Solution
  • Question 22
    1 / -0
    If a resistance of 100 , an inductance of 0.5 H and a capacitance of 10 x 10−6 F are connected in series with a 50 Hz AC supply, then what will be the impedance?
    Solution
  • Question 23
    1 / -0
    A coil of 1200 turns and mean area 500 cm2 is held perpendicular to a uniform magnetic field of induction 4 × 10-4 H. The resistance of the coil is 20 ohms. When the coil is rotated through 180° in the magnetic field in 0.1 s, what is the average electric current (in mA) induced?
    Solution
    In perpendicular position in uniform magnetic field, magnetic field linked with the each turn of coil = BA
    On rotating coil through 180°, flux linked = -BA
    ∴ Change in magnetic flux = -2BA
    ∴ emf induced in the coil e = -N
    =

    where N is the number of turns in the coil.
    The current in the coil



    =
    = 2400 × 10-5
    = 24 × 10-3 A
    = 24 mA
  • Question 24
    1 / -0
    In a transformer, the output current and voltage are 4A and 20 V respectively. If the ratio of number of turns in primary to secondary is 2 : 1, what are the input current and voltage?
    Solution
    vO = 20 v
    IO = 4
    = or = [Transformation ratio]
    Vo = (Vi) or Vi = 40 v
    Input voltage = 40 v
    Also, Vi Ii = VO IO
    Or 40 (Ii) = (20) (4)
    Or Ii = 2 ampere
  • Question 25
    1 / -0
    The impedance of an AC circuit, which contains a capacitive reactance of 5 ohms and inductive reactance of 8 ohms, will be
    Solution
    Impedance X = ?
    Inductive Reactance XL = 8 ohms
    Capacitive Reactance XC = 5 ohms
    X = XL - Xc
    X = 8 - 5 = 3 ohms
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