Question

One Pico farad is Equal to-
(A). \[{{10}^{-24}}\text{ F}\]
(B). \[{{10}^{-18}}\text{ F}\]
(C). \[{{10}^{-12}}\text{ F}\]
(D). \[{{10}^{-6}}\text{ F}\]

Answer 1

Hint: Pico is one of the prefixes used before units to represent the number of parts of a unit. Farad is the SI unit of capacitance. \[1\text{ pF}\] is used to denote the number of parts of farad. All prefixes denote parts in the powers of 10. The unit of Farad tells us how much a conductor can store charge inside it.

Complete step-by-step answer:
Farad is the SI unit of Capacitance. It is denoted by \[\text{F}\] .
Capacitance is the ratio of amount of charge stored in a conductor to the potential difference applied across it’s ends. In simpler words, capacitance is the measure of capacity of a conductor to store charge inside it. It is given by-
 \[\text{C = }\dfrac{\text{Q}}{{{\text{V}}_{\text{a}}}\text{-}{{\text{V}}_{\text{b}}}}\]
Where \[\text{Q}\] is the charge stores in the conductor and ( \[{{\text{V}}_{\text{a}}}\text{-}{{\text{V}}_{\text{b}}}\] ) is the potential difference.
In the metric system, different prefixes are used to denote parts of a unit. Similarly Pico is a prefix which is added before the unit when there are \[{{10}^{-12}}\] parts of a unit. Therefore,
 \[\begin{align}
  & \text{1 }\!\!\mu\!\!\text{ F = 1}{{\text{0}}^{-6}}\text{ F} \\
 & \text{1 }\!\!\mu\!\!\text{ F = 1}{{\text{0}}^{6}}\text{ pF} \\
 & \Rightarrow \text{ 1 pF = 1}{{\text{0}}^{-12}}\text{ F} \\
\end{align}\]
So, \[\text{pF}\] is one millionth ( \[{{10}^{-12}}\] ) of a Farad. Hence, the correct option is (C). \[{{10}^{-12}}\text{ F}\]

So, the correct answer is “Option C”.

Note: Other metric units are Mega ( \[{{10}^{6}}\] ), Kilo ( \[{{10}^{3}}\] ), Hecto ( \[{{10}^{2}}\] ), Decca ( \[10\] ), Deci ( \[{{10}^{-1}}\] ), Centi ( \[{{10}^{-2}}\] ), Milli ( \[{{10}^{-3}}\] ) etc. Avoid calculation mistakes as it can render the prefix wrong. In order to move from a smaller part to a bigger part we divide, whereas when we move from a bigger part to a smaller part we multiply.