1.At what frequency does the inductive reactance of a 42.0 µH inductor equal the
ID: 1702358 • Letter: 1
Question
1.At what frequency does the inductive reactance of a 42.0 µH inductor equal the capacitive reactance of a 42.0 µF capacitor?(a) What is the maximum current in a 3.80 µF capacitor when it is connected across a North American electrical outlet having ?Vrms = 120 V, f = 60.0 Hz?
mA
(b) What is the maximum current when it is connected across a European electrical outlet having ?Vrms = 240 V and f = 50.0 Hz?
mA
c) -An AC power supply produces a maximum voltage ?Vmax = 90 V. This power supply is connected to a 26.0 O resistor, and the current and resistor voltage are measured with an ideal AC ammeter and voltmeter. What does each meter read? Note that an ideal ammeter has zero resistance and that an ideal voltmeter has infinite resistance.
1- V
2- A
Explanation / Answer
Inductance L = 42* 10 ^ -6 H Capacitance C = 42* 10 ^ -6 F Inductive reactance = Capacitive reactance Lw = 1/ Cw w^ 2 = 1/ LC w = 1 / sqrt (LC ) = 1/( 42* 10 ^ -6 ) required frequency f = w / 2*pi = 3789.4 Hz (a). Capacitance C = 3.8 * 10 ^ -6 F Vrms = 120 V frequency f = 60 Hz Capacitive reactance X = 1/ Cw = 1/ ( C* 2*pi* f) = 698 ohm rms current i rms = V rms / X = 0.1719 A So, maximum current I = i rms * sqrt ( 2) = 0.2431 A = 243.1 mA (b). similarly you this (c). Vmax = 90 V resistance R = 26.0 Ohm maximum current I = V max / R = 3.46 A rms current i = I / sqrt 2 = 2.447 A rms voltage V = Vmax / sqrt2 = 63.63 volt So,. volt meter reading = 63.63 volt ammeter reading = 2.447 A
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