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Lv 4
? 發問於 科學及數學其他 - 科學 · 1 十年前

AL phy (urgent!!)

1. http://entertainment.webshots.com/photo/2213353500... and V2 are identical high resistance a.c. voltmeters. Explain why the sum of the r.m.s. p.d.s. measured across AB and BC by V1 and V2 exceeds the applied r.m.s. p.d. of 150 V. Calculate the value of C. 2. A heating coil, of resistance 100Ω, a choke (of negligible resistance) with an inductance of 0.5H and a capacitor of capacitance 15uF, are connected in series aross 200V, 50Hz mains.Calculate (a) the impedance of the circuit, (b) the current taken from the mains, (c) the potential drop across the carious components in the circuit(d) the power factor of the circuit and (e) the energy converted by the heating coil in one cycle 3. In a RCL series circuit, at what frequency will the circuit through the circuit be minimum? Explain

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  • 1 十年前
    最愛解答

    1) Since in AC circuit, there exists a phase difference between the p.d. arcoss the resistor and the capacitor. Thus the sum of their p.d. cannot be directly calculated by simply adding their values.

    Also since C and R have the same r.m.s. p.d. across them, reactance of C should be equal to the resistace of R, i.e.

    1/(2π x 50C) = 500

    C = 1/(2π x 50 x 500) = 6.37 μF

    2a) Inductive reactance = 2π x 50 x 0.5 = 157.1 Ω

    Capacitative reactance = 1/(2π x 50 x 15 x 10-6) = 212.2 Ω

    So the reactive component is capacitative with value = 212.2 - 157.1 = 55.1 Ω

    Impedancet = √(1002 + 55.12) = 114.2 Ω

    b) Current = 200/114.2 = 1.75 A with a phase lead to the mains voltage.

    c) Across the resistance = 1.75 x 100 = 175 V

    Across the choke = 1.75 x 157.1 = 275 V

    Across the capacitance = 1.75 x 212.2 = 372 V

    d) Looking back into the impedance:

    Resistive component = 100 Ω

    Impedance = 114.2 Ω

    Power factor = 100/114.2 = 0.876

    e) 1 cycle = 0.02 s

    Hence energy converted = 0.02 x 1752/100 = 6.125 J

    3) For a RCL series circuit, the impedance is given by:

    Z = √[R2 + (ω2L2 - 1/(ω2C2))] where ω = 2π x freq.

    So to minimize current, we should maximize Z in which:

    when freq. is zero, the circuit actually becomes an open circuit since the capacitative reactance is infinity.

    資料來源: Myself
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