What voltage is needed to create a current of 43 mA in a circuit containing only a 1.3-μF capacitor, when the frequency is 3.9 kHz? Note: Th

Question

What voltage is needed to create a current of 43 mA in a circuit containing only a 1.3-μF capacitor, when the frequency is 3.9 kHz? Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise.

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Ngọc Diệp 5 months 2021-08-19T09:05:16+00:00 1 Answers 0 views 0

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    2021-08-19T09:06:52+00:00

    Answer:

    1.35 V

    Explanation:

    Given:

    Capacitance of the capacitor (C) = 1.3 μF = 1.3\times 10^{-6}\ F\ \ [1\mu F=10^{-6}\ F]

    Frequency (f) = 3.9 kHz= 3.9 × 1000 Hz = 3900 Hz [1 kHz = 1000 Hz]

    Current flowing in the circuit (I) = 43 mA = 0.043 A [1 mA = 0.001 A]

    Now, as only capacitor is there in the circuit, the impedance of the circuit is equal to the reactance of the capacitor.

    So, Z=X_C

    The reactance of the capacitor is given as:

    X_C=\frac{1}{2\pi fC}

    Plug in the values given and solve for X_C. This gives,

    X_C=\frac{1}{2\pi\times 3900\times 1.3\times 10^{-6}}\\\\X_C=31.39\ \Omega

    Therefore, the impedance is, Z=31.39\ \Omega

    Now, the voltage needed to create the given current is obtained using the formula from Ohm’s law and is given as:

    V=IZ\\\\V=(0.043\ A)(31.39\ \Omega)\\\\V=1.35\ V

    Therefore, the voltage needed to create a current of 43 mA is 1.35 V.

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