Problem 14.97

กำหนดให้ \(C_{1} = 30 μF, C_{2} = 20 μF, R_{1} = 60 Ω\) และ \(R_{2} = 30 Ω\)

พิจารณาในกรณีไม่มีกระแสไฟฟ้าไหลผ่านตัวเก็บประจุ

จาก \(I = \frac{ε}{R + r}\)

\(I =\frac{ε}{R_{1} + R_{2}}; r = 0 Ω\)

\(IR_{1} =\frac{εR_{1}}{R_{1} + R_{2}}\)

\(\frac{Q}{C}=\frac{εR_{1}}{R_{1} + R_{2}}\)

\(Q =\frac{εR_{1}C}{R_{1} + R_{2}}\)

\(Q =\frac{εR_{1}}{R_{1} + R_{2}}(\frac{C_{1}C_{2}}{C_{1} + C_{2}})\)

\(\frac{Q}{C_{1}}=\frac{εR_{1}C_{2}}{(R_{1} + R_{2})C_{1} + C_{2}}\)

\(\Delta V_{AB}=\frac{(12 V)(60 Ω)(20 \mu F)}{(60 + 30 Ω)(30 + 20 \mu F)}\)

\(\Delta V_{AB}= 3.2 V \;\blacksquare\)