Physics · Textbook solutions

AC Circuits

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 39 questions

13. AC Circuits — worked examples

8 q

Solved Examples

Worked · 8
  1. Solved Ex.13.1
    An alternating voltage is given by e=6sin⁡(100πt)e = 6 \sin (100\pi t). find (i) the peak value (ii) frequency (iii) time period and (iv) instantaneous value at time t=2t = 2 ms
  2. Solved Ex.13.2
    An alternating voltage given by e=140sin⁡3142 te = 140 \sin 3142\, t is connected across a pure resistor of 50 Ω\Omega. Find (i) the frequency of the source (ii) the rms current through the resistor.
  3. Solved Ex.13.3
    An inductor of inductance 200 mH is connected to an AC source of peak emf 210 V and frequency 50 Hz. Calculate the peak current. What is the instantaneous voltage of the source when the current is at its peak value?
  4. Solved Ex.13.4
    4. A Capacitor of 2 μ\muF is connected to an AC source of emf e=250sin⁡100πte = 250 \sin 100\pi t. Write an equation for instantaneous current through the circuit and give reading of AC ammeter connected in the circuit.
  5. Solved Ex.13.5
    A 100 mH inductor, a 25 μ\muF capacitor and a 15 Ω\Omega resistor are connected in series to a 120 V, 50 Hz AC source. Calculate (i) impedance of the circuit at resonance (ii) current at resonance (iii) resonant frequency
  6. Solved Ex.13.6
    A coil of 0.01 H inductance and 1 Ω\Omega resistance is connected to 200 V, 50 Hz AC supply. Find the impedance of the circuit and time lag between maximum alternating voltage and current.
  7. Solved Ex.13.7
    A 100 Ω\Omega resistor is connected to a 220 V rms, 50 Hz supply (i) What is the rms value of current in the circuit? (ii) What is the net power consumed over a full cycle?
  8. Solved Ex.13.8
    A sinusoidal voltage of peak value 283 V and frequency 50 Hz is applied to a series LCR circuit in which R=3 ΩR = 3\ \Omega, L=25.48L = 25.48 mH and C=796 μC = 796\ \muf. Find i) The impedance of the circuit ii) The phase difference between the voltage across source and the currents iii) The power factor iv) The power dissipated in the surface

Exercises

31 q

Choose the correct option

Practice · 5
  1. Choose the correct option.
    Ex Q.1 (i)
    If the rms current in a 50 Hz AC circuit is 5A, the value of the current 1/3001/300 seconds after its value becomes zero is
    1. A.
      525\sqrt{2} A
    2. B.
      5325\sqrt{\frac{3}{2}} A
    3. C.
      56\frac{5}{6} A
    4. D.
      52\frac{5}{\sqrt{2}} A
  2. Ex Q.1 (ii)
    A resistor of 500 Ω\Omega and an inductance of 0.5 H are in series with an AC source which is given by V=1002sin⁡(1000 t)V = 100\sqrt{2} \sin (1000\, t). The power factor of the combination is
    1. A.
      12\frac{1}{\sqrt{2}}
    2. B.
      13\frac{1}{\sqrt{3}}
    3. C.
      0.5
    4. D.
      0.6
  3. Ex Q.1 (iii)
    In a circuit L, C & R are connected in series with an alternating voltage of frequency f. the current leads the voltage by 45∘45^\circ. The value of C is
    1. A.
      1πf(2πfL−R)\frac{1}{\pi f \left( 2\pi f L - R \right)}
    2. B.
      12πf(2πfL−R)\frac{1}{2\pi f \left( 2\pi f L - R \right)}
    3. C.
      1πf(2πfL+R)\frac{1}{\pi f \left( 2\pi f L + R \right)}
    4. D.
      12πf(2πfL+R)\frac{1}{2\pi f \left( 2\pi f L + R \right)}
  4. Ex Q.1 (iv)
    In an AC circuit, e and i are given by e=150sin⁡(150t)e = 150 \sin (150 t) V and i=150sin⁡(150 t+π3)i = 150 \sin \left( 150\, t + \frac{\pi}{3} \right) A. the power dissipated in the circuit is
    1. A.
      106W
    2. B.
      150W
    3. C.
      5625W
    4. D.
      Zero
  5. Ex Q.1 (v)
    In a series LCR circuit the phase difference between the voltage and the current is 45∘45^\circ. Then the power factor will be
    1. A.
      0.607
    2. B.
      0.707
    3. C.
      0.808
    4. D.
      1

Answer in brief

Practice · 5
  1. Answer in brief.
    Ex Q.2 (i)
    An electric lamp is connected in series with a capacitor and an AC source is glowing with a certain brightness. How does the brightness of the lamp change on increasing the capacitance ?
  2. Ex Q.2 (ii)
    The total impedance of a circuit decreases when a capacitor is added in series with L and R. Explain why ?
  3. Ex Q.2 (iii)
    For very high frequency AC supply, a capacitor behaves like a pure conductor. Why ?
  4. Ex Q.2 (iv)
    What is wattless current ?
  5. Ex Q.2 (v)
    What is the natural frequency of L C circuit ? What is the reactance of this circuit at this frequency

Solve the following

Practice · 21
  1. Ex Q.3
    In a series LR circuit XL=RX_L = R and power factor of the circuit is P1P_1. When capacitor with capacitance C such that XL=XCX_L = X_C is put in series, the power factor becomes P2P_2. Calculate P1/P2P_1 / P_2.
  2. Ex Q.4
    When an AC source is connected to an ideal inductor show that the average power supplied by the source over a complete cycle is zero.
  3. Ex Q.5
    Prove that an ideal capacitor in an AC circuit does not dissipate power
  4. Ex Q.6
    (a) An emf e=e0sin⁡ωte = e_0 \sin \omega t applied to a series L - C - R circuit derives a current I=I0sin⁡ωtI = I_0 \sin \omega t in the circuit. Deduce the expression for the average power dissipated in the circuit. (b) For circuits used for transporting electric power, a low power factor implies large power loss in transmission. Explain
  5. Ex Q.7
    A device Y is connected across an AC source of emf e=e0sin⁡ωte = e_0 \sin \omega t. The current through Y is given as i=i0sin⁡(ωt+π/2)i = i_0 \sin \left( \omega t + \pi/2 \right) a) Identify the device Y and write the expression for its reactance. b) Draw graphs showing variation of emf and current with time over one cycle of AC for Y. c) How does the reactance of the device Y vary with the frequency of the AC ? Show graphically d) Draw the phasor diagram for the device Y.
  6. Ex Q.8
    Derive an expression for the impedance of an LCR circuit connected to an AC power supply.
  7. Ex Q.9
    Compare resistance and reactance.
  8. Ex Q.10
    Show that in an AC circuit containing a pure inductor, the voltage is ahead of current by π/2\pi/2 in phase.
  9. Ex Q.11
    An AC source generating a voltage e=e0sin⁡ωte = e_0 \sin \omega t is connected to a capacitor of capacitance C. Find the expression for the current ii flowing through it. Plot a graph of ee and ii versus ωt\omega t.
  10. Ex Q.12
    If the effective current in a 50 cycle AC circuit is 5 A, what is the peak value of current? What is the current 1/6001/600 sec. after if was zero ?
  11. Ex Q.13
    A light bulb is rated 100W for 220 V AC supply of 50 Hz. Calculate (a) resistance of the bulb. (b) the rms current through the bulb.
  12. Ex Q.14
    A 15.0 μ\muF capacitor is connected to a 220 V, 50 Hz source. Find the capacitive reactance and the current (rms and peak) in the circuit. If the frequency is doubled, what will happen to the capacitive reactance and the current.
  13. Ex Q.15
    An AC circuit consists of only an inductor of inductance 2 H. If the current is represented by a sine wave of amplitude 0.25 A and frequency 60 Hz, calculate the effective potential difference across the inductor (π=3.142)( \pi = 3.142 )
  14. Ex Q.16
    Alternating emf of e=220sin⁡100πte = 220 \sin 100\pi t is applied to a circuit containing an inductance of (1/π)(1/\pi) henry. Write an equation for instantaneous current through the circuit. What will be the reading of the AC galvanometer connected in the circuit?
  15. Ex Q.17
    A 25 μ\muF capacitor, a 0.10 H inductor and a 25 Ω\Omega resistor are connected in series with an AC source whose emf is given by e=310sin⁡314 te = 310 \sin 314\, t (volt). What is the frequency, reactance, impedance, current and phase angle of the circuit?
  16. Ex Q.18
    A capacitor of 100 μ\muF, a coil of resistance 50 Ω\Omega and an inductance 0.5 H are connected in series with a 110 V-50Hz source. Calculate the rms value of current in the circuit.
  17. Ex Q.19
    Find the capacity of a capacitor which when put in series with a 10 Ω\Omega resistor makes the power factor equal to 0.5. Assume an 80V-100Hz AC supply.
  18. Ex Q.20
    Find the time required for a 50 Hz alternating current to change its value from zero to the rms value.
  19. Ex Q.21
    Calculate the value of capacitance in picofarad, which will make 101.4 micro henry inductance to oscillate with frequency of one megahertz.
  20. Ex Q.22
    A 10 μ\muF capacitor is charged to a 25 volt of potential. The battery is disconnected and a pure 100 m H coil is connected across the capacitor so that LC oscillations are set up. Calculate the maximum current in the coil.
  21. Ex Q.23
    A 100 μ\muF capacitor is charged with a 50 V source supply. Then source supply is removed and the capacitor is connected across an inductance, as a result of which 5A current flows through the inductance. Calculate the value of the inductance.