Convert ampere • hour to Elementary Charge
Learn how to convert
1
ampere • hour to
Elementary Charge
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(ampere \times hour\right)={\color{rgb(20,165,174)} x}\left(Elementary \text{ } Charge\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(coulomb\right)\)
\(\text{Left side: 1.0 } \left(ampere \times hour\right) = {\color{rgb(89,182,91)} 3.6 \times 10^{3}\left(coulomb\right)} = {\color{rgb(89,182,91)} 3.6 \times 10^{3}\left(C\right)}\)
\(\text{Right side: 1.0 } \left(Elementary \text{ } Charge\right) = {\color{rgb(125,164,120)} 1.602176487 \times 10^{-19}\left(coulomb\right)} = {\color{rgb(125,164,120)} 1.602176487 \times 10^{-19}\left(C\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(ampere \times hour\right)={\color{rgb(20,165,174)} x}\left(Elementary \text{ } Charge\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 3.6 \times 10^{3}} \times {\color{rgb(89,182,91)} \left(coulomb\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.602176487 \times 10^{-19}}} \times {\color{rgb(125,164,120)} \left(coulomb\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 3.6 \times 10^{3}} \cdot {\color{rgb(89,182,91)} \left(C\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.602176487 \times 10^{-19}} \cdot {\color{rgb(125,164,120)} \left(C\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 3.6 \times 10^{3}} \cdot {\color{rgb(89,182,91)} \cancel{\left(C\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.602176487 \times 10^{-19}} \times {\color{rgb(125,164,120)} \cancel{\left(C\right)}}\)
\(\text{Conversion Equation}\)
\(3.6 \times 10^{3} = {\color{rgb(20,165,174)} x} \times 1.602176487 \times 10^{-19}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 1.602176487 \times 10^{-19} = 3.6 \times 10^{3}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{1.602176487 \times 10^{-19}}\right)\)
\({\color{rgb(20,165,174)} x} \times 1.602176487 \times 10^{-19} \times \dfrac{1.0}{1.602176487 \times 10^{-19}} = 3.6 \times 10^{3} \times \dfrac{1.0}{1.602176487 \times 10^{-19}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1.602176487}} \times {\color{rgb(99,194,222)} \cancel{10^{-19}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1.602176487}} \times {\color{rgb(99,194,222)} \cancel{10^{-19}}}} = 3.6 \times 10^{3} \times \dfrac{1.0}{1.602176487 \times 10^{-19}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{3.6 \times 10^{3}}{1.602176487 \times 10^{-19}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-19}}\text{ can be rewritten to }10^{19}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{19} \times 3.6 \times 10^{3}}{1.602176487}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{22} \times 3.6}{1.602176487}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx2.246943473 \times 10^{22}\approx2.2469 \times 10^{22}\)
\(\text{Conversion Equation}\)
\(1.0\left(ampere \times hour\right)\approx{\color{rgb(20,165,174)} 2.2469 \times 10^{22}}\left(Elementary \text{ } Charge\right)\)
