Question

Three capacitors are connected in parallel to a battery with a total capacitance of 0.7 farads. The first capacitor is rated at 0.2 farads, and the second at 0.4 farads.

(a) Find the capacitance of the third capacitor.
(b) Draw an appropriate circuit diagram.

Answer 1

The capacitance of the third capacitor when three capacitors with a total capacitance of 0.7F are connected in parallel, with the first two being 0.2F and 0.4F respectively, is 0.1F. A circuit diagram would show these capacitors in parallel, connected to a battery.

Step-by-step explanation:

We have three capacitors connected in parallel to a battery with a total capacitance of 0.7 farads. The first capacitor has a capacitance of 0.2 farads, and the second has a capacitance of 0.4 farads.

Capacitance of the Third Capacitor

The total capacitance, CT, for capacitors in parallel is the sum of their individual capacitances:

CT = C1 + C2 + C3

Given CT = 0.7 farads, C1 = 0.2 farads, and C2 = 0.4 farads, we can solve for C3:

0.7 F = 0.2 F + 0.4 F + C3

C3 = 0.7 F - 0.2 F - 0.4 F

C3 = 0.1 F

So the capacitance of the third capacitor is 0.1 farads.

Circuit Diagram

To draw an appropriate circuit diagram:

1. Connect three capacitor symbols in parallel lines.
2. Connect these capacitors to the two terminals of the battery symbol.
3. Label the capacitors with their respective capacitances, i.e., C1 = 0.2F, C2 = 0.4F, and C3 = 0.1F.