Question

Find the charge on capacitor, C2 , in the diagram below if V_ab=24.0 volts,〖 C〗_1=6.00 μF,〖 C〗_2= 3.00 μF,and C_3=10.0 μF.

Answer 1

The charge on the capacitor 2 (C₂) is 48μF.

Analysis of the circuit diagram

In the circuit diagram, C₁ and C₂ are in series connection, while C₃ is parallel to C₁ and C₂.

• Same charge flows in a series arrangement (charge on C₁ = charge on C₂).
• Same voltage flows in a parallel arrangement (voltage on C₁, C₂ = voltage on C₃).

Charge on capacitor C₁ and C₂

$Q_1 = Q_2 = Q\\\\V = \frac{Q}{C_1} + \frac{Q}{C_2} \\\\V = Q(\frac{1}{C_1}+ \frac{1}{C_2} )\\\\V = Q(\frac{C_2 + C_1}{C_1 C_2} )\\\\Q = V(\frac{C_1 C_2}{C_2+ C_1} )\\\\Q = 24 \times (\frac{6\times 10^{-6} \times 3 \times 10^{-6}}{6\times 10^{-6} \ + \ 3\times 10^{-6}} )\\\\Q = \frac{4.32 \times 10^{-10}}{9\times 10^{-6}} \\\\Q = 4.8\times 10^{-5} \ C\\\\Q = 48 \ \mu C$

Thus, the charge on the capacitor 2 (C₂) is 48μF.

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