Capacitor C1 is in series with capacitors C2 and C3 in parallel. Then three capacitor system is connected to battery with V0. Determine the

Question

Capacitor C1 is in series with capacitors C2 and C3 in parallel. Then three capacitor system is connected to battery with V0. Determine the charge stored by C1 when C1 = 20 μF, C2 = 10 μF, C3 = 30 μF, and V0 = 18 V.g

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Thanh Hà 4 years 2021-08-07T18:44:19+00:00 1 Answers 15 views 0

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  1. thuhuong
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    2021-08-07T18:45:23+00:00
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    Answer:

      Q₁ = 2.4 10⁻⁴ C

    Explanation:

    We have a circuit with several capacitors, let’s find the equivalent capacitor of the parallel

        C_{eq1} = C₂ + C₃

        C_{eq1} = (10 +30) 10⁻⁶

        C_{eq1} = 40 10⁻⁶ F

    There remains a series system between C₁ and C_{eq1}, let’s find the equivalent capacitor

         1/C_{eq2} = 1 / C₁ + 1 / C_{eq1}

         1 /C_{eq2} = 1 / 20 10⁻⁶ + 1/40 10⁻⁶

         1 / C_{eq2} = 0.075 10⁶

         C_{eq2} = 13.33 10⁻⁶ F

    let’s use the relationship

            V = Q / C_{eq2}

            Q = V C_{eq2}

            Q = 18  13.33 10⁻⁶

            Q = 2.4 10⁻⁴ C

    In a combination of capacitors in series the charge is constant, so the charge on C₁ is the same

            Q₁ = 2.4 10⁻⁴ C

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