Question #319404

1. Using the definition C = Q/V, show that for a SERIES connection of capacitors:



1/C1/C1+1/C2. What does this equation mean? What happens to C as more and more capacitors are connected in series? 2. Using the definition C = QV, show that for a PARALLEL connection of capacitors: C = C1 + C2. What does this equation mean? What happens to C as more and more capacitors are connected in parallel?

1
Expert's answer
2022-03-28T11:02:23-0400

1. For series connection

Q1=Q2=Q,V1+V2=VQ_1=Q_2=Q,\quad V_1+V_2=V

Hence

V=V1+V2=Q1C1+Q1C1=QCV=V_1+V_2=\frac{Q_1}{C_1}+\frac{Q_1}{C_1}=\frac{Q}{C}

Finally

1C1+1C1=1C\frac{1}{C_1}+\frac{1}{C_1}=\frac{1}{C}

2. For parallel connection

Q1+Q2=Q,V1=V2=VQ_1+Q_2=Q,\quad V_1=V_2=V

Hence

C1V1+C2V2=CVC_1V_1+C_2V_2=CV

Finally

C1+C2=CC_1+C_2=C


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