Question

Find the charge on and the potential difference across each

Answer 1

To solve this we need to find the equivalent capacitance of the set of capacitors. The first step is to re-draw the circuit so that C1is drawn vertically - this makes it more obvious what's in parallel or series.

Now contract the circuit from 4 capacitors to 1.

Step 1 - C2 and C3 are in series. Replace this pair by a single capacitor C23:

1/C23 = 1/C2 + 1/C3 = 1/90 + 1/45 = 3/90.

Therefore C23 = 90/3 = 30 pF.

Step 2 - C1 and C23 are in parallel. Replace that pair by a single capacitor C123 = 90 + 30 = 120 pF.

Step 3 - C4 and C123 are in series. Replace that pair by a single capacitor Ceq:

1/Ceq = 1/C4 + 1/C123 = 1/120 + 1/120 = 2/120

Ceq = 120/2 = 60 pF

Step 4 - Determine the charge on Ceq.

Q = Ceq ΔV = 60 pF * 12 V = 720 pC.

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