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Three capacitors of capacitance C1 = 3.85 𝜇F, C2 = 2.20 𝜇F, and C3 = 4.95 𝜇F are connected in series. A potential difference of ΔVb = 84.0 V is maintained by a battery.Find the equivalent capacitance of the series of capacitors and the charge on each capacitor.Ceq  =  𝜇FQ  =  𝜇CDetermine the effect on the equivalent capacitance of reducing the second capacitance to 0.1 times its previous value.Ceq

Question

Three capacitors of capacitance C1 = 3.85 𝜇F, C2 = 2.20 𝜇F, and C3 = 4.95 𝜇F are connected in series. A potential difference of ΔVb = 84.0 V is maintained by a battery.Find the equivalent capacitance of the series of capacitors and the charge on each capacitor.Ceq  =  𝜇FQ  =  𝜇CDetermine the effect on the equivalent capacitance of reducing the second capacitance to 0.1 times its previous value.Ceq

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Solution

The equivalent capacitance (Ceq) for capacitors in series is given by the reciprocal of the sum of the reciprocals of the individual capacitances. So,

1/Ceq = 1/C1 + 1/C2 + 1/C3

Substituting the given values:

1/Ceq = 1/3.85 + 1/2.20 + 1/4.95

Solving this gives:

1/Ceq = 0.2597 + 0.4545 + 0.2020

1/Ceq = 0.9162

Therefore, Ceq = 1 / 0.9162 = 1.091 μF

The charge (Q) on each capacitor in a series circuit is the same and is given by Q = Ceq * ΔVb. Substituting the given values:

Q = 1.091 μF * 84.0 V = 91.644 μC

If the second capacitance is reduced to 0.1 times its previous value, it becomes 0.22 μF. The new equivalent capacitance is then:

1/Ceq_new = 1/3.85 + 1/0.22 + 1/4.95

Solving this gives:

1/Ceq_new = 0.2597 + 4.5454 + 0.2020

1/Ceq_new = 5.0071

Therefore, Ceq_new = 1 / 5.0071 = 0.200 μF

So, reducing the second capacitance to 0.1 times its previous value decreases the equivalent capacitance of the series.

This problem has been solved

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