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Physics · Textbook solutions

Alternating Current

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 18 questions

Worked Examples

10 q

Solved Examples

Worked · 10
  1. Eg 7.1
    A light bulb is rated at 100 W100\,\text{W} for a 220 V220\,\text{V} supply. Find (a) the resistance of the bulb; (b) the peak voltage of the source; and (c) the rms current through the bulb.
  2. Eg 7.2
    A pure inductor of 25.0 mH25.0\,\text{mH} is connected to a source of 220 V220\,\text{V}. Find the inductive reactance and rms current in the circuit if the frequency of the source is 50 Hz50\,\text{Hz}.
  3. Eg 7.3
    A lamp is connected in series with a capacitor. Predict your observations for dc and ac connections. What happens in each case if the capacitance of the capacitor is reduced?
  4. Eg 7.4
    A 15.0 μF15.0\,\mu\text{F} capacitor is connected to a 220 V220\,\text{V}, 50 Hz50\,\text{Hz} source. Find the capacitive reactance and the current (rms and peak) in the circuit. If the frequency is doubled, what happens to the capacitive reactance and the current?
  5. Eg 7.5
    A light bulb and an open coil inductor are connected to an ac source through a key as shown in Fig. 7.9. The switch is closed and after sometime, an iron rod is inserted into the interior of the inductor. The glow of the light bulb (a) increases; (b) decreases; (c) is unchanged, as the iron rod is inserted. Give your answer with reasons.
  6. Eg 7.6
    A resistor of 200 Ω200\,\Omega and a capacitor of 15.0 μF15.0\,\mu\text{F} are connected in series to a 220 V220\,\text{V}, 50 Hz50\,\text{Hz} ac source. (a) Calculate the current in the circuit; (b) Calculate the voltage (rms) across the resistor and the capacitor. Is the algebraic sum of these voltages more than the source voltage? If yes, resolve the paradox.
  7. Eg 7.7
    (a) For circuits used for transporting electric power, a low power factor implies large power loss in transmission. Explain. (b) Power factor can often be improved by the use of a capacitor of appropriate capacitance in the circuit. Explain.
  8. Eg 7.8
    A sinusoidal voltage of peak value 283 V283\,\text{V} and frequency 50 Hz50\,\text{Hz} is applied to a series LCRLCR circuit in which R=3 ΩR = 3\,\Omega, L=25.48 mHL = 25.48\,\text{mH}, and C=796 μFC = 796\,\mu\text{F}. Find (a) the impedance of the circuit; (b) the phase difference between the voltage across the source and the current; (c) the power dissipated in the circuit; and (d) the power factor.
  9. Eg 7.9
    Suppose the frequency of the source in the previous example can be varied. (a) What is the frequency of the source at which resonance occurs? (b) Calculate the impedance, the current, and the power dissipated at the resonant condition.
  10. Eg 7.10
    At an airport, a person is made to walk through the doorway of a metal detector, for security reasons. If she/he is carrying anything made of metal, the metal detector emits a sound. On what principle does this detector work?

Exercises

8 q
  1. Ex 7.1
    A 100 Ω100\,\Omega resistor is connected to a 220 V220\,\text{V}, 50 Hz50\,\text{Hz} ac supply. (a) What is the rms value of current in the circuit? (b) What is the net power consumed over a full cycle?
  2. Ex 7.2
    (a) The peak voltage of an ac supply is 300 V300\,\text{V}. What is the rms voltage? (b) The rms value of current in an ac circuit is 10 A10\,\text{A}. What is the peak current?
  3. Ex 7.3
    A 44 mH44\,\text{mH} inductor is connected to 220 V220\,\text{V}, 50 Hz50\,\text{Hz} ac supply. Determine the rms value of the current in the circuit.
  4. Ex 7.4
    A 60 μF60\,\mu\text{F} capacitor is connected to a 110 V110\,\text{V}, 60 Hz60\,\text{Hz} ac supply. Determine the rms value of the current in the circuit.
  5. Ex 7.5
    In Exercises 7.3 and 7.4, what is the net power absorbed by each circuit over a complete cycle. Explain your answer.
  6. Ex 7.6
    A charged 30 μF30\,\mu\text{F} capacitor is connected to a 27 mH27\,\text{mH} inductor. What is the angular frequency of free oscillations of the circuit?
  7. Ex 7.7
    A series LCRLCR circuit with R=20 ΩR = 20\,\Omega, L=1.5 HL = 1.5\,\text{H} and C=35 μFC = 35\,\mu\text{F} is connected to a variable-frequency 200 V200\,\text{V} ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?
  8. Ex 7.8
    Figure 7.17 shows a series LCRLCR circuit connected to a variable frequency 230 V230\,\text{V} source. L=5.0 HL = 5.0\,\text{H}, C=80 μFC = 80\,\mu\text{F}, R=40 ΩR = 40\,\Omega. (a) Determine the source frequency which drives the circuit in resonance. (b) Obtain the impedance of the circuit and the amplitude of current at the resonating frequency. (c) Determine the rms potential drops across the three elements of the circuit. Show that the potential drop across the LCLC combination is zero at the resonating frequency.