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.
            In Nepal, AC mains supply has RMS voltage 220 V. Peak voltage is
            📅CEE MBBS 2025
            Q2.
            Phase difference between current and voltage in LCR circuit:
            📅CEE MBBS 2024B
            Q3.
            The ratio of mean value over one half cycle to the rms of a.c. of complete cycle is:
            📅CEE MBBS 2024B
            Q4.
            In a capacitive circuit:
            📅CEE MBBS 2024a
            Q5.
            If \(f=50\,\text{Hz}\) and \(E=220\,\text{V}\), then in an LCR circuit the voltage may be more than 220 V across:
            📅CEE MBBS 2023
            Q6.
            Frequency of AC in Nepal is:
            📅CEE MBBS 2022
            Q7.
            Power is transmitted from a power house at high-voltage AC because:
            📅CEE MBBS 2022
            Q8.
            The self-inductance of the motor of an electric fan is 10 H. In order to impart maximum power of 50 Hz, it should be connected to a capacitance of:
            📅CEE BDS 2024
            Q9.
            The ratio of mean value over one half cycle to the rms value of a.c. of complete cycle:
            📅CEE BDS 2024
            Q10.
            The phase difference between the current and voltage in LCR circuit at resonance is:
            📅CEE BDS 2024
            Q11.
            A wire of mass 200 kg has capacitance 0.0014 μF/kg and frequency 50 kHz. Then what is the inductance when impedance is minimum?
            📅CEE BDS 2021
            Q12.
            Which one is quality factor?
            📅BP 2013
            Q13.
            In RC circuit, charge on capacitor (when being discharged) is maximum at
            📅BP 2013
            Q14.
            A circuit has resonance frequency f. If capacitance is doubled then new frequency of circuit is:
            Q15.
            A door metal detector uses a principle based on
            📅BP 2011
            Q16.
            A coil of inductance \(8.4 mH\) and resistance \(6\Omega\) is connected to a \(12V\) battery. The current in the coil is \(1A\) at approx. time?
            📅BP 2009
            Q17.
            An emf of \(15\,\mathrm V\) is applied to a coil of inductance \(5\,\mathrm H\) and resistance \(10\,\Omega\). Find the ratio \(I(\infty)/I(1\,\mathrm s)\).
            📅BP 2009
            Q18.
            In LCR circuit having L=\(8H\), C=\(0.5\)\muF and R=\(100\Omega\) connected in series produces natural angular frequency
            📅MOE 2014
            Q19.
            The AC voltage is E=\(100\)\sqrt2 cos100t volt is connected to a capacitor of capacitance \(10\)\muF. The current flowing through the capacitor is
            📅MOE 2014
            Q20.
            At resonance, the impedance of a series LCR circuit is:
            📅2012•2013•2012,13
            Q21.
            The average power of LCR circuit dissipated through AC circuit is:
            📅MOE 2010
            Q22.
            In Nepal, the supply of AC voltage is \(220V\). The peak voltage is
            📅MOE 2010
            Q23.
            In a purely resistive A.C circuit, the current:
            📅KU 2014
            Q24.
            In LR circuit
            📅KU 2010
            Q25.
            An inductive coil has resistance of \(100\Omega\) 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
            Q26.
            The resonant frequency of a LCR series circuit having L=\(8H\), C=\(0.5\)\muF and R=\(100\Omega\) is;
            📅IE 2011
            Q27.
            Power dissipation in AC circuit depends upon
            📅IE 2013
            Q28.
            An AC supply gives \(30V\) RMS which is fed on a pure resistance of \(10\Omega\), the power dissipated in this is;
            📅IE 2013
            Q29.
            Admittance of an alternating circuit is defined as reciprocal of
            📅MOE 2009
            Q30.
            A wire of mass 200kg has capacitance \(0.0014\)\muF/kg and frequency 50KHz. Then what is the inductance when impedance is minimum?
            📅IOM 2066
            Q31.
            An a.c. having angular frequency \(1000\) rad/sec is passed through a capacitor of \(1\)\muF, then capacitive reactance is....
            📅KU.08
            Q32.
            Power dissipated in pure inductor of inductance 'L' when current 'I' passes through it is
            Q33.
            In an a.c. circuit V_{rms}=\(100V\); capacitance \(20\)\muF, current \(0.628A\), the frequency of a.c. is
            📅MOE 2056
            Q34.
            For fixed capacitance, which change decreases capacitive reactance \(X_C\) in an AC circuit?
            📅MOE 2053
            Q35.
            In an A.C circuit capacitance is \(20\)\muF, inductance is \(500mH\) and resistance is \(40\Omega\). If \(2.5\) Amperes current flows in the circuit then the power delivered in the circuit is:
            📅MOE 2060
            Q36.
            Capacitative reactance for dc is
            📅MOE 2058
            Q37.
            If the capacitance is increased, then
            📅IE-05
            Q38.
            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
            Q39.
            A choke coil should have
            📅BPKIHS-08
            Q40.
            In a LCR Circuit, Inductor, Capacitor and Resistor are in series working at \omega=\(1\)/\sqrt(LC) and emf V_{\(0\)}. Then the sum of potential dropped across inductor and capacitor is
            📅IE-06
            Q41.
            In a series combination of R, L and C to an ac source at resonance, if R=\(20\Omega\), then impedance of the combination is
            📅MOE 2010
            Q42.
            Laminated cores are used in transformers to
            Q43.
            An induction coil is used to
            Q44.
            In an AC circuit, the electrical energy is dissipated in
            Q45.
            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
            Q46.
            In a circuit, the value of the a.c. is measured by hot wire ammeter is \(10\) ampere. Its peak value will be
            Q47.
            A sinusoidal AC current flows through a resistance. If the peak current is I_{\(0\)}, then power dissipated is
            Q48.
            A highly inductive circuit has a power factor which is
            Q49.
            For \(L=8\,\mathrm H\), \(C=0.5\,\mu\mathrm F\), and \(R=100\,\Omega\) in series, what is the resonant angular frequency?
            Q50.
            The reactance of a capacitance at \(50Hz\) is \(50\Omega\). If the frequency is increased to \(100Hz\), the new reactance is:
            Q51.
            An ac circuit consists of a resistance \(4\Omega\) and reactance \(3\Omega\). The combination connected to a potential of \(10V\). The current flowing in the circuit will be
            Q52.
            In a circuit I is given by I = I_{\(1\)} sin(\omegat - \pi/\(2\)) when AC potential of E = E_{\(0\)} sin\omegat has been applied. Then the power consumption P in the circuit would be:
            Q53.
            Alternating voltage V=\(400\) sin(\(500\)\pit) is applied across a resistance of \(0\).2k\Omega. The rms value of current will be equal to
            Q54.
            An alternating voltage E=\(200\)\sqrt2 sin100t volt is connected to a \(1\)\muF capacitor through an AC ammeter. The reading of the ammeter is
            📅MOE 2014
            Q55.
            An applied voltage \(V=220\sin(100t)\,\mathrm V\) drives a circuit with impedance \(Z=110\,\Omega\) and phase difference \(60^\circ\). Find average power.
            Q56.
            In an ac circuit voltage V and current i are given by V=\(100\) sin100t volts, i=\(100\) sin(100t+\pi/\(3\)) mA. The power dissipated in the circuit is
            Q57.
            If resistance in an ac circuit is increased, then its power factor:
            Q58.
            An LCR circuit with R=\(100\Omega\) 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:
            Q59.
            An alternating current is given by equation I = I_{\(1\)}cos\omegat + I_{\(2\)}sin\omegat. The r.m.s. value of current is given by:
            Q60.
            In the non-resonant circuit, what will be the nature of the circuit for frequencies higher than the resonant frequency?
            Q61.
            The power factor of a series RL circuit is \(0.5\). If R=\(100\Omega\), f=\(50Hz\), then L is
            Q62.
            An ac source is \(120V\)-\(60Hz\). The value of voltage after \(1\)/\(720\) sec from start will be:
            Q63.
            A coil having an inductance of \(1\)/\pi H is connected in series with a resistance of \(30\Omega\). \(20V\)-\(200Hz\) AC source is impressed across the combination, the phase angle between voltage and current is
            Q64.
            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?
            Q65.
            An LR circuit consists of a resistance of \(50\Omega\) and a coil of inductive reactance \(120\Omega\). If the circuit is connected across \(26V\) a.c. mains, the current in the circuit is
            Q66.
            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?
            Q67.
            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
            Q68.
            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?
            Q69.
            An A.C. Circuit contains resistance \(4\Omega\) and capacitive reactance \(3\Omega\). Then, the impedance of circuit is
            📅IOM 2016•KU 2017•IOM 2016, KU 2017