Capacitor Capacitors are devices that store electric charge. The charge is released at a later time when it is needed. Capacitors when not mounted on an electronic board. Capacitance • A capacitor consist of two conductors of any shape, placed near, but not touching one another. Often the space between the conductors is filled with an electrically insulating material. • Each plate carries a charge of the same magnitude, one being positive, while the other is negative. • The charge that is stored on the plates of a capacitor is proportional to the potential difference across the plates. Thus where is proportionality constant called capacitance. The capacitance is defined as an ability of the capacitor to store an electrical charge. The unit of capacitance is the farad (1 F = 1 CV-1). One farad is a very large unit and in practice, capacitances are normally much less than this. Some common capacitances are: + Battery Capacitor Capacitors in series Capacitors in series all carry the same charge which is equal to the charge on 𝑒𝑞 . The sum of the potential difference across each capacitor is equal to the potential difference across From 𝑞 𝑞 𝑞 𝑞 + + = 𝐶 𝐶 𝐶 𝐶 𝒆𝒒. Capacitors in parallel q1 q2 q3 V q V V The voltage across each capacitor is the same, which is also equal to the voltage across the equivalent capacitance. The charge in each capacitor is not the same i.e. However, the total charge on all the individual capacitors is the same as the charge that would be stored on a single equivalent capacitor i.e. but then Energy stored in a Capacitor Charging a capacitor requires energy. The work done in completely charging a capacitor where is the average voltage across the plates during charging. If the final voltage is is given by then and the work done is which is stored as electric potential energy in the capacitor. Since . the energy stored is Capacitor and equivalent capacitance Example 1.9: The equivalent capacitance of a combination of capacitors For the arrangement shown alongside, calculate (a) the single equivalent capacitance, C1 = 10 μF (b) the p.d. across the 10 μF capacitor, (c) the energy stored in the 2 μF capacitor. (a) 𝐶 = 𝐶 + 𝐶 = 2 + 3 = 5 𝜇𝐹 1 1 1 + = 𝐶 𝐶 𝐶 1 1 1 3 + = = 10 5 𝐶 10 1 3 = 𝐶 10 10 𝐶 = = 3.33 𝜇𝐹 3 (b) 𝑞 = 𝐶 𝑉 = 3.33 × 10 × 100 𝑞 = 3.33 × 10 𝐶 𝑞 = 𝑞 = 𝑞 so 𝑞 =3.33 × 10 𝐶 𝑞 3.33 × 10 ∴𝑉 = = = 33.3 𝑉 𝐶 10 × 10 C2 = 2 μF C3 = 3 μF V = 100 V (c) 𝑉 + 𝑉 = 100 𝑉 = 100 − 𝑉 = 100 − 33.3 = 66.7 𝑉 𝑉 = 𝑉 = 𝑉 = 66.7 𝑉 ∴𝑊 = 𝐶 𝑉 𝑊 = × 2 × 10 × 66.7 𝑊 = 4.45 × 10 𝐽