45Alternating current

📚
ALTERNATING CURRENT
▢ Definition:
❖ Statement: Alternating current changes continuously in magnitude and periodically in direction
❖ Representation:
  • •
    Can be represented by sine curve
  • •
    Can be represented by cosine curve
❖ **table:
    ❖ Symbols:
      ◈ **type: bullet
    1. \(I\) = instantaneous value of AC
    2. \(I_0\) = peak value / amplitude of current
    3. \(E\) = instantaneous value of alternating emf
    4. \(E_0\) = peak value / amplitude of emf
    5. \(f\) = frequency
    6. \(T\) = time period
    7. \(\omega\) = angular frequency
    ▢ Mean or Average Value of AC:
    ❖ Reason: AC is positive during first half cycle and negative during next half cycle, so average value over one complete cycle is zero
    ❖ Defined For: Half cycle only
    ❖ Definition: Value of steady current which sends same charge through circuit in half cycle as AC sends in same time
    ❖ **table:
      ◈ caption: Mean Value of Alternating EMF
      ◈ data:
        1. Interval
        2. Mean / Average EMF
        1. First half cycle \((0\to T/2)\)
        2. \(E_m=E*{av}=\frac{2E_0}{\pi}=0.637E_0\)
        1. Second half cycle \((T/2\to T)\)
        2. \(E_m=E*{av}=-\frac{2E_0}{\pi}=-0.637E_0\)
        1. Complete cycle \((0\to T)\)
        2. \(E_m=E*{av}=0\)
    ▢ Root Mean Square Value:
    ❖ Also Called:
      ◈ **type: bullet
    1. Effective value
    2. Virtual value
    ❖ Definition: RMS value of AC is the value of steady current which produces same heat in given resistance in given time as AC produces in same resistance in same time
    ❖ **table:
      ▢ Important AC Measurement Points:

      Table 1: AC Measurement

      Fact
      Answer
      AC instruments measure
      RMS value
      If AC value nature is not mentioned
      Assume RMS current or RMS emf
      Ohmic resistance in AC
      Behaves same as in DC circuit
      ▢ Reactance:
      ❖ Symbol: \(X\)
      ❖ Definition: Opposition offered by coil or capacitor or both to flow of alternating current
      ❖ Cause: Arises due to inductive and capacitive effects
      ❖ Phase Relation: Across reactance, alternating voltage and current do not remain in same phase
      ❖ Unit: Ohm \((\Omega)\)
      ❖ Types:
        ◈ **type: bullet
      1. Inductive reactance \((X_L)\)
      2. Capacitive reactance \((X_C)\)
      ❖ **table:
        ▢ AC Through Pure Resistor:
        ❖ Condition: Circuit contains resistance \(R\) only
        ❖ Behaviour: Current and voltage remain in same phase
        ❖ **table:
          ❖ Graph:
            ◈ **type: bullet
          1. Current and voltage curves are in phase
          2. Current becomes maximum when voltage becomes maximum
          3. Current becomes zero when voltage becomes zero
          ▢ High-Yield Recall:
          ❖ **table:
            Q1.
            Which one is quality factor? [BP 2013]
            📅BP 2013
            Q2.
            In RC circuit, charge on capacitor (when being discharged) is maximum at [BP 2013]
            📅BP 2013
            Q3.
            A circuit has resonance frequency f. If capacitance is doubled then new frequency of circuit is:
            Q4.
            A door metal detector uses a principle based on [BP 2011]
            📅BP 2011
            Q5.
            A coil of inductance 8.4 mH and resistance 6Ω is connected to a 12V battery. The current in the coil is 1A at approx. time? [BP 2009]
            📅BP 2009
            Q6.
            An emf of 15 volt is applied in a circuit coil containing 5 Henry inductance and 10Ω resistance. The ratio of the current at time t=∞ and at t=1 sec is [BP 2009]
            📅BP 2009
            Q7.
            In LCR circuit having L=8H, C=0.5μF and R=100Ω connected in series produces natural angular frequency [MOE 2014]
            📅MOE 2014
            Q8.
            The AC voltage is E=100√2 cos100t volt is connected to a capacitor of capacitance 10μF. The current flowing through the capacitor is [MOE 2014]
            📅MOE 2014
            Q9.
            At resonance condition the effective resistance in LCR series circuit is [2012,13]
            📅2012•2013
            Q10.
            The average power of LCR circuit dissipated through AC circuit is: [MOE 2010]
            📅MOE 2010
            Q11.
            In Nepal, the supply of AC voltage is 220V. The peak voltage is [MOE 2010]
            📅MOE 2010
            Q12.
            In a purely resistive A.C circuit, the current: [KU 2014]
            📅KU 2014
            Q13.
            In LR circuit [KU 2010]
            📅KU 2010
            Q14.
            An inductive coil has resistance of 100Ω when an AC of frequency 100Hz is fed to coil, applied voltage leads the current by 45°, the inductance of the coil is approximately; [IE 2010]
            📅IE 2010
            Q15.
            The resonant frequency of a LCR series circuit having L=8H, C=0.5μF and R=100Ω is; [IE 2011]
            📅IE 2011
            Q16.
            Power dissipation in AC circuit depends upon [IE 2013]
            📅IE 2013
            Q17.
            An AC supply gives 30V RMS which is fed on a pure resistance of 10Ω, the power dissipated in this is; [IE 2013]
            📅IE 2013
            Q18.
            Admittance of an alternating circuit is defined as reciprocal of [MOE 2009]
            📅MOE 2009
            Q19.
            A wire of mass 200kg has capacitance 0.0014μF/kg and frequency 50KHz. Then what is the inductance when impedance is minimum? [IOM 2066]
            📅IOM 2066
            Q20.
            An a.c. having angular frequency 1000 rad/sec is passed through a capacitor of 1μF, then capacitive reactance is.... [KU.08]
            📅KU.08
            Q21.
            Power dissipated in pure inductor of inductance 'L' when current 'I' passes through it is
            Q22.
            In an a.c. circuit Vrms=100V; capacitance 20μF, current 0.628A, the frequency of a.c. is [MOE 2056]
            📅MOE 2056
            Q23.
            You and your friends are listening to the radio. Your friends wants to decrease the capacitive reactance XC of the radio transistor. [MOE 2053]
            📅MOE 2053
            Q24.
            In an A.C circuit capacitance is 20μF, inductance is 500mH and resistance is 40Ω. If 2.5 Amperes current flows in the circuit then the power delivered in the circuit is: [MOE 2060]
            📅MOE 2060
            Q25.
            Capacitative reactance for dc is [MOE 2058]
            📅MOE 2058
            Q26.
            If the capacitance is increased, then [IE-05]
            📅IE-05
            Q27.
            The inductance L and a resistance R are connected in series with a battery of emf E. Find the maximum rate at which energy is stored in the magnetic field. [BPKIHS-95]
            📅BPKIHS-95
            Q28.
            A choke coil should have [BPKIHS-08]
            📅BPKIHS-08
            Q29.
            In a LCR Circuit, Inductor, Capacitor and Resistor are in series working at ω=1/√(LC) and emf V0. Then the sum of potential dropped across inductor and capacitor is [IE-06]
            📅IE-06
            Q30.
            In a series combination of R, L and C to an ac source at resonance, if R=20Ω, then impedance of the combination is [MOE 2010]
            📅MOE 2010
            Q31.
            Laminated cores are used in transformers to
            Q32.
            An induction coil is used to
            Q33.
            In an AC circuit, the electrical energy is dissipated in
            Q34.
            A 20 volt ac is applied to a circuit consisting of a resistance and a coil with negligible resistance. If the voltage across the resistance is 12 volt, the voltage across the coil is
            Q35.
            In a circuit, the value of the a.c. is measured by hot wire ammeter is 10 ampere. Its peak value will be
            Q36.
            A sinusoidal AC current flows through a resistance. If the peak current is I0, then power dissipated is
            Q37.
            A highly inductive circuit has a power factor which is
            Q38.
            If an LCR circuit contains L=8H, C=0.5μF, R=100Ω in series, then the resonant frequency will be
            Q39.
            The reactance of a capacitance at 50Hz is 50Ω. If the frequency is increased to 100Hz, the new reactance is:
            Q40.
            An ac circuit consists of a resistance 4Ω and reactance 3Ω. The combination connected to a potential of 10V. The current flowing in the circuit will be
            Q41.
            In a circuit I is given by I = I1 sin(ωt - π/2) when AC potential of E = E0 sinωt has been applied. Then the power consumption P in the circuit would be:
            Q42.
            Alternating voltage V=400 sin(500πt) is applied across a resistance of 0.2kΩ. The rms value of current will be equal to
            Q43.
            An alternating voltage E=200√2 sin100t volt is connected to a 1μF capacitor through an AC ammeter. The reading of the ammeter is [MOE 2014]
            📅MOE 2014
            Q44.
            In an AC circuit, voltage applied is V=220 sin100t. If the impedance is 110Ω and phase difference between current and voltage is 60°, the power consumption is equal to
            Q45.
            In an ac circuit voltage V and current i are given by V=100 sin100t volts, i=100 sin(100t+π/3) mA. The power dissipated in the circuit is
            Q46.
            If resistance in an ac circuit is increased, then its power factor:
            Q47.
            An LCR circuit with R=100Ω is connected to an ac source 100V, 50Hz. The magnitude of the phase difference between current and voltage becomes 30°, When either C is removed or when L is removed. The power dissipated in LCR circuit is:
            Q48.
            An alternating current is given by equation I = I1cosωt + I2sinωt. The r.m.s. value of current is given by:
            Q49.
            In the non-resonant circuit, what will be the nature of the circuit for frequencies higher than the resonant frequency?
            Q50.
            The power factor of a series RL circuit is 0.5. If R=100Ω, f=50Hz, then L is
            Q51.
            An ac source is 120V-60Hz. The value of voltage after 1/720 sec from start will be:
            Q52.
            A coil having an inductance of 1/π H is connected in series with a resistance of 30Ω. 20V-200Hz AC source is impressed across the combination, the phase angle between voltage and current is
            Q53.
            A resistor, an inductor and a capacitor are connected in series to an ac power supply. When measured with the help of an ac voltmeter the voltages across them are found to be 80V, 30V and 90V respectively. What is the supply voltage?
            Q54.
            An LR circuit consists of a resistance of 50Ω and a coil of inductive reactance 120Ω. If the circuit is connected across 26V a.c. mains, the current in the circuit is
            Q55.
            A pure resistance and a pure inductance are connected in series across a 100 volt AC line. A voltmeter gives the same reading whether connected across resistance or inductance. What does it read?
            Q56.
            In an oscillating LC circuit the maximum charge on the capacitor is Q. The charge on the capacitor when the energy is stored equally between the electric and magnetic field is
            Q57.
            If A and B are identical bulbs, which bulb glows brighter in the circuit shown?
            Q58.
            In the circuit shown, voltmeter reads 100V. Then L is:
            Q59.
            In the circuit shown, the resonance frequency is: [BPKIHS]
            📅BPKIHS
            Q60.
            In the circuit shown, the initial value of current through the battery on closing the circuit (i.e. K pressed) is
            Q61.
            If an alternating current of frequency 50Hz is flowing through a conducting wire, then how many times does the current becomes zero in one second?
            Q62.
            An A.C. Circuit contains resistance 4Ω and capacitive reactance 3Ω. Then, the impedance of circuit is [IOM 2016, KU 2017]
            📅IOM 2016•KU 2017