CHAPTER 6: ALTERNATING CURRENT
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1 CHAPTER 6: ALTERNATING CURRENT PSPM II 2005/2006 NO. 12(C) 12. (c) An ac generator with rms voltage 240 V is connected to a RC circuit. The rms current in the circuit is 1.5 A and leads the voltage by 60. (i) Draw a phasor diagram for the RC circuit. (ii) Calculate the value of resistance, R. [Ans: R = 80 Ω] PSPM II 2006/2007 NO A 0.7 H inductor and a 150 Ω resistor are connected in series to an AC source of rms voltage 230 V and frequency 50 Hz. Calculate (a) the reactance of the inductor. [Ans: X L = Ω = 70π] (b) the impedance of the circuit. [Ans: Z = Ω] PSPM II 2006/2007 NO. 12(C) 12. (c) A 500-turn AC generator coil of cross-sectional area m 2 is rotated at a rate of 1500 rpm in a uniform magnetic field of T. (i) Calculate the peak value of the induced emf. [Ans: V 0 = V] (ii) Calculate the rms value of the induced emf. [Ans: V rms = V] (iii) Sketch the output voltage. PSPM II 2007/2008 NO A full-wave rectified voltage is connected to a resistor. (a) Sketch a V-t graph of the rectified voltage. (b) Suggest a circuit diagram that will smoothen the rectified voltage. (c) Sketch a V-t graph of the output voltage of your circuit. PSPM II 2007/2008 NO. 12(C) 12. (c) An alternating source 220 V, 50 Hz is applied to a coil with inductance 0.14 H and resistance 12 Ω. Calculate (i) the current in the coil. [Ans: I = A] (ii) the phase angle between the current and source voltage. [Ans: θ = ] PCH 1
2 PSPM II 2008/2009 NO FIGURE 3 FIGURE 3 shows the variation of current and voltage against time in a circuit. (a) Sketch the current and voltage phasor diagram. (b) Calculate the power delivered to the circuit. [Ans: P = 433 W] PSPM II 2008/2009 NO. 12(B) 12. (b) A voltage of 230 V, 50 Hz is connected in series to a 100 mh inductor and a 300 Ω resistor. Calculate the (i) peak voltage. [Ans: V P = V] (ii) rms current in the circuit. [Ans: I rms = A] (iii) potential difference across the inductor. [Ans: V L = V] (iv) power factor of the circuit. [Ans: cos φ = 0. 99] (v) average power. [Ans: P ave = W] [10 marks] PSPM II 2009/2010 NO (a) (i) Why do the average values of alternating voltage and alternating current give very little information about their actual behavior? (ii) Why does root mean square current useful? (b) Calculate the peak voltage of an electric circuit if it is connected to a 240 V AC source. [Ans: V 0 = V] PSPM II 2009/2010 NO (a) Why an ideal LC circuit does not consume any power? [1 mark] PCH 2
3 (b) How do the resistance, capacitive reactance and inductive reactance change when the frequency in a circuit is decreased? Explain your answer. (c) A circuit is made up of a 3200 pf capacitor connected in series to a 30 μh coil of resistance 4 Ω. Calculate (i) impedance at frequency 30 khz. [Ans: Z = 1652 Ω] (ii) resonant frequency. [Ans: f 0 = Hz] (d) The current in an AC circuit lags the voltage by 45. Determine the circuit components. Explain your answer. [3 marks] PSPM II 2010/2011 NO FIGURE 3 FIGURE 3 shows the graph of an alternating current. (a) Write down the current equation. [Ans: I = 10 sin(314t) = 10 sin(100πt)] (b) Calculate the rms current value. [Ans: I rms = A] PSPM II 2011/2012 NO (a) FIGURE 4 An AC source has an output voltage of V = 300 sin ωt. The source is connected to a 120 Ω resistor as in FIGURE 4. (i) Calculate the rms voltage. [Ans: V rms = 212 V] PCH 3
4 (ii) Calculate the rms current in the resistor. [Ans: I rms = A] (iii) Calculate the average power delivered to the circuit. [Ans: P = 375 W] (iv) What is the rms voltage if the frequency is doubled? [Ans: The rms voltage remains the same.] [7 marks] (b) An AC source that has a peak voltage of 120 V and a frequency of 50.0 Hz is connected in series to a 900 Ω resistor, a 2.40 H inductor and a 10.0 μf capacitor. Calculate (i) the impedance of the circuit. [Ans: Z = 1000 Ω] (ii) the phase angle of the circuit. [Ans: φ = ] (iii) the power factor of the circuit. [Ans: cos φ = 0. 90] [8 marks] PSPM II 2012/2013 NO (a) In an AC circuit, the supply voltage is given by V = 240 sin (5000t + π ) where V in 2 volt and the current is given by I = sin(5000t) where I in ampere and t in second. (i) What is meant by root mean square (rms) value of the current? (ii) Calculate the impedance of the circuit. [Ans: Z = 500 Ω] (iii) Sketch the phasor diagram for V and I and state the electrical component either RCL, RC or RL. Give your reason. (iv) Calculate the instantaneous and maximum power dissipated in the circuit. [Ans: P inst = sin 10000t ; P max = W] [9 marks] (b) A resistor of 6 Ω, a capacitor of 3000 μf and an inductor of 5 mh are connected in series. If an AC source of 50 Hz and peak voltage of 240 V is connected to this circuit combination, calculate (i) (ii) the total impedance of the circuit. [Ans: Z = Ω] the resonance frequency of the circuit and explain the energy dissipated during the resonance. [Ans: f resonance = Hz] PSPM II 2013/2014 NO (a) A voltmeter shows a reading of 220 V for a 50 Hz AC voltage. (i) Calculate the maximum value of the AC voltage. [Ans: V max = 311 V] (ii) Write the equation for the AC voltage. [Ans: V = 311 sin 100πt] (b) A 0.9 kω resistor, 0.25 μc capacitor and 2.5 H inductor are connected in series across a 240 Hz AC source with 140 V peak voltage. (i) Calculate the impedance. [Ans: Z = Ω] (ii) Calculate the maximum current. [Ans: I max = A] (iii) Calculate the phase angle between the current and voltage. [Ans: φ = ] (iv) Which quantity lags: current or voltage? Explain your answer. (v) How to achieve resonance in the circuit? [11 marks] PCH 4
5 PSPM II 2014/2015 NO (a) An RL series circuit with a H inductor and 250 Ω resistor is connected with a source of peak voltage 240 V at the frequency 200 Hz. Calculate the (i) inductive reactance of the circuit. [Ans: X L = Ω] (ii) impedance of the circuit. [Ans: Z = Ω] (iii) Power factor for this circuit. [Ans: cos φ = ] (iv) rms voltage of the source. [Ans: V rms = V] (v) Average power delivered by the source. [Ans: P ave = W] (b) An RLC circuit consists of a 40 Ω resistor, a 22 mh inductor and a 400 nf capacitor connected in series to the AC source which has a peak voltage of 100 mv and a frequency of 1.6 khz. (i) Calculate the capacitive reactance. [Ans: X C = Ω] (ii) Calculate the rms current. [Ans: I rms = ma] (iii) Determine the phase angle. [Ans: φ = ] (iv) Sketch the phasor diagram to represent the voltages across the components and the source. [9 marks] PCH 5
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