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26 May, 12:10

A capacitor is connected to an ac generator that has a frequency of 2.3 kHz and produces a rms voltage of 1.5 V. The rms current in the capacitor is 31 mA. When the same capacitor is connected to a second ac generator that has a frequency of 4.8 kHz, the rms current in the capacitor is 85 mA. What rms voltage does the second generator produce

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  1. 26 May, 15:38
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    Given that,

    AC frequency of 2.3KHz

    f=2.3*10³Hz

    Vrms produce is

    Vrms=1.5V

    Current rms

    Irms = 31mA

    The capacitor is reconnected to a generator of frequency

    f=4.8KHz = 4800Hz

    The current rms becomes

    Irms = 85mA

    Vrms=?

    Solution

    First genrator

    The capacitive reactance is given as

    Xc=Vrms/Irms

    Xc=1.5/31*10^-3

    Xc=48.39 ohms

    Now, to know the capacitance of the capacitor

    Xc=1/2πfC

    Then,

    C=1/2πfXc

    So,

    C=1/2*π*2300*48.39

    C=1.43*10^-6C

    C=1.43μF

    Note: the capacitance of the capacitor did not change,

    Now for generator two.

    The reactance are given as

    Xc=1/2πfC

    Xc=1/2*π*4800*1.43*10^-6

    Xc=23.19ohms

    Then,

    Vrms2=Irms2 * Xc

    Vrms2=85*10^-3*23.19ohms

    Vrms2=1.97V

    Vrms2=1.97Volts
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