Problem 15: Find the charge on 5 µF capacitor in the circuit shown:

Solution

Let C₁ = 3 µF
C₂ = 2 µF and
C₃ = 5 µF.
From the figure, C₂ and C₃ are in parallel. Therefore, by the formula for the equivalent capacitance of capacitors in parallel,
C_2,3 = 2 + 5 = 7 µF

Now this capacitor is in series with C₁ and by the formula for the equivalent capacitance for series combination

So the equivalent capacitance of the circuit is

To calculate charge on the equivalent capacitance of the circuit, C_e,
Q = 2.1 × 6 = 12.6 µF The voltage drop across the capacitance

This is the voltage across the parallel combination of C₂ and C₃. Now we can calculate charge on C₃.
Q₃ = 5 × 1.8 = 9.0 µF       Answer