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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,
C2,3 = 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, Ce,
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

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