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
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.
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