Calculate the charge appearing on each of the three capacitors shown in the diagram.

Question

Quantrex Academy · Accepted Answer

Correct answer: B. 48 on the 8 capacitor and 24 on each of the 4 capacitors

From the given circuit diagram, capacitors B and C are in parallel.

Equivalent capacitance of B and C is:

C_{BC} = 4 \mu\text{F} + 4 \mu\text{F} = 8 \mu\text{F}

Capacitor A is in series with this parallel combination. The equivalent capacitance of the entire circuit is:

C_{eq} = \dfrac{8 \times 8}{8 + 8} = 4 \mu\text{F}

Total charge drawn from the battery is:

Q = C_{eq}V = 4 \mu\text{F} \times 12 \text{ V} = 48 \mu\text{C}

Since capacitor A is in the main branch, the charge on the

8 \mu\text{F}

capacitor is

48 \mu\text{C}

.

This charge of

48 \mu\text{C}

distributes equally between the two identical

4 \mu\text{F}

capacitors in parallel.

Charge on each

4 \mu\text{F}

capacitor is:

q = \dfrac{48 \mu\text{C}}{2} = 24 \mu\text{C}

Calculate the charge appearing on each of the three capacitors...