Question
Asked Nov 10, 2019
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Consider the combination of capacitors shown in the figure.(Figure 1) Three capacitors are connected to each other in series, and then to the battery. The values of the capacitances are C, 2C, and 3C, and the applied voltage is ΔV. Initially, all of the capacitors are completely discharged; after the battery is connected, the charge on plate 1 is Q.

Find the voltage ΔV1 across the first capacitor.
Express your answer in terms of ΔV.
 
Find the charge Q on the first capacitor.
Express your answer in terms of C and ΔV1.
 
Using the value of Q just calculated, find the equivalent capacitance Ceq for this combination of capacitors in series.
Express your answer in terms of C.
C
2C
3C
1 2
+Q
3 4
5 6
Δν
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C 2C 3C 1 2 +Q 3 4 5 6 Δν

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Expert Answer

Step 1

Given:

Charge on the capacitors = Q

The relation between charge and capacitor:

C = QV………………(i)

Step 2

Let the voltage drop across the capacitor C, 2C and 3C be delta V1, delta V2 and delta V3 respectively.

Therefore:

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AV = AV, + AV, +AV,... (i) ...i)

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Step 3

Voltage drop across...

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-Q = CAV Δ ρ ΔV 2C CAW -Δ 2C 2 CAVΔν. Δν 3C 3C

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