Question

calculate the capacitance of a system that stores 1.0 × 10^{-10} c of charge at 100.0 v. use c = \frac{q}{\delta v}.

a. 1.0 × 10^{12} f
b. 1.0 × 10^{-12} f
c. 1.0 × 10^{8} f
d. 1.0 × 10^{-8} f

Explanation:

Step1: Substitute the given values into the formula

Given \(Q = 1.0\times10^{- 10}\text{ C}\) and \(\Delta V=100.0\text{ V}\), and the formula \(C=\frac{Q}{\Delta V}\).
Substitute the values: \(C=\frac{1.0\times 10^{-10}}{100.0}\).

Step2: Simplify the expression

\(C=\frac{1.0\times 10^{-10}}{1.0\times10^{2}}=1.0\times10^{-12}\text{ F}\) (using the rule \(\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}\)).

Answer:

B. \(1.0\times 10^{-12}\text{ F}\)