Question #313154

2. The capacitors have values C₁ = 2.0 μF and C₂ = 4.0 μF, C₂ = 5.0 μF C4 = 7.0 μF and the potential difference across the battery is 9.0 V. Assume that the capacitors are connected in series.

a) Find the equivalent capacitance of the circuit.

b) Solve for the potential difference across each capacitors.


3. Given the same problem in #2. Assume that the capacitors are connected in parallel.

a) Find the equivalent capacitance of the circuit.

b) Solve for the charge across each capacitors.


1
Expert's answer
2022-03-18T12:01:45-0400

(a)

1C=1C1+1C2+1C3+1C4\frac{1}{C}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+\frac{1}{C_4}

1C=12+14+15+17\frac{1}{C}=\frac{1}{2}+\frac{1}{4}+\frac{1}{5}+\frac{1}{7}

1C=70+35+28+20140\frac{1}{C}=\frac{70+35+28+20}{140}

C=153140=1.09μFC=\frac{153}{140}=1.09\mu F

(b)Charge

Q=CVQ=CV

Q=1.09×106×9=9.84μCQ=1.09\times10^{-6}\times9=9.84\mu C

V1=9.84×1062×106=4.92VV_1=\frac{9.84\times10^{-6}}{2\times10^{-6}}=4.92V

V2=9.84×1064×106=2.46VV_2=\frac{9.84\times10^{-6}}{4\times10^{-6}}=2.46V

V3=9.84×1065×106=1.968VV_3=\frac{9.84\times10^{-6}}{5\times10^{-6}}=1.968V

V4=9.84×1067×106=1.40VV_4=\frac{9.84\times10^{-6}}{7\times10^{-6}}=1.40V

3(a)

Ceq=C1+C2+C3+C4C_{eq}=C_1+C_2+C_3+C_4


Ceq=(2+4+5+7)×106=18×106CC_{eq}=(2+4+5+7)\times10^{-6}=18\times10^{-6}C

(b)

Charge


Q1=C1VQ1=2×9×106C=18μCQ_1=C_1V\\Q_1=2\times9\times10^{-6}C=18\mu C

Q2=C2VQ2=4×9×106C=36μCQ_2=C_2V\\Q_2=4\times9\times10^{-6}C=36\mu C

Q3=C3VQ3=5×9×106C=45μCQ_3=C_3V\\Q_3=5\times9\times10^{-6}C=45\mu C

Q4=C4VQ4=7×9×106C=63μCQ_4=C_4V\\Q_4=7\times9\times10^{-6}C=63\mu C

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