three capacitors are connected in series to an ac voltage source with amplitude 12.0 V and frequency 6.3 kHz. What are the peak voltages acr

Question

three capacitors are connected in series to an ac voltage source with amplitude 12.0 V and frequency 6.3 kHz. What are the peak voltages across each capacitor

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RI SƠ 4 months 2021-09-05T05:53:34+00:00 1 Answers 4 views 0

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    2021-09-05T05:55:01+00:00

    Answer:

    The peak voltages across each capacitor are 6.0 V, 4.0 V and 2.0 V.

    Explanation:

    Given that,

    Amplitude = 12.0 V

    Frequency = 6.3 kHz

    Suppose, Three capacitors are 2.0 μF, 3.0 μF and 6.0 μF

    We need to calculate the equivalent capacitor

    Using formula of series

    \dfrac{1}{C}=\dfrac{1}{C_{1}}+\dfrac{1}{C_{2}}+\dfrac{1}{C_{3}}

    Put the value into the formula

    \dfrac{1}{C}=\dfrac{1}{2.0}+\dfrac{1}{3.0}+\dfrac{1}{6.0}

    \dfrac{1}{C}=1

    C=1\ \mu F

    We need to calculate the charge

    Using formula of charge

    q=CV

    Put the value into the formula

    q=1\times12.0

    q=12\ \mu C

    The charge will be same in each capacitor because the capacitors are connected in series.

    We need to calculate the voltage across first capacitor

    Using formula of voltage

    V_{1}=\dfrac{q}{C_{1}}

    Put the value into the formula

    V_{1}=\dfrac{12}{2.0}

    V_{1}=6.0 V

    We need to calculate the voltage across second capacitor

    Using formula of voltage

    V_{2}=\dfrac{q}{C_{2}}

    Put the value into the formula

    V_{2}=\dfrac{12}{3.0}

    V_{2}=4.0 V

    We need to calculate the voltage across third capacitor

    Using formula of voltage

    V_{3}=\dfrac{q}{C_{3}}

    Put the value into the formula

    V_{3}=\dfrac{12}{6.0}

    V_{3}=2.0 V

    Hence, The peak voltages across each capacitor are 6.0 V, 4.0 V and 2.0 V.

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