Convert EMU of charge to ampere • hour
Learn how to convert
1
EMU of charge to
ampere • hour
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(EMU \text{ } of \text{ } charge\right)={\color{rgb(20,165,174)} x}\left(ampere \times hour\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(coulomb\right)\)
\(\text{Left side: 1.0 } \left(EMU \text{ } of \text{ } charge\right) = {\color{rgb(89,182,91)} 10.0\left(coulomb\right)} = {\color{rgb(89,182,91)} 10.0\left(C\right)}\)
\(\text{Right side: 1.0 } \left(ampere \times hour\right) = {\color{rgb(125,164,120)} 3.6 \times 10^{3}\left(coulomb\right)} = {\color{rgb(125,164,120)} 3.6 \times 10^{3}\left(C\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(EMU \text{ } of \text{ } charge\right)={\color{rgb(20,165,174)} x}\left(ampere \times hour\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 10.0} \times {\color{rgb(89,182,91)} \left(coulomb\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 3.6 \times 10^{3}}} \times {\color{rgb(125,164,120)} \left(coulomb\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 10.0} \cdot {\color{rgb(89,182,91)} \left(C\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 3.6 \times 10^{3}} \cdot {\color{rgb(125,164,120)} \left(C\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 10.0} \cdot {\color{rgb(89,182,91)} \cancel{\left(C\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 3.6 \times 10^{3}} \times {\color{rgb(125,164,120)} \cancel{\left(C\right)}}\)
\(\text{Conversion Equation}\)
\(10.0 = {\color{rgb(20,165,174)} x} \times 3.6 \times 10^{3}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\({\color{rgb(255,204,153)} \cancel{10.0}} = {\color{rgb(20,165,174)} x} \times 3.6 \times {\color{rgb(255,204,153)} \cancelto{10^{2}}{10^{3}}}\)
\(\text{Simplify}\)
\(1.0 = {\color{rgb(20,165,174)} x} \times 3.6 \times 10^{2}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 3.6 \times 10^{2} = 1.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{3.6 \times 10^{2}}\right)\)
\({\color{rgb(20,165,174)} x} \times 3.6 \times 10^{2} \times \dfrac{1.0}{3.6 \times 10^{2}} = \times \dfrac{1.0}{3.6 \times 10^{2}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{3.6}} \times {\color{rgb(99,194,222)} \cancel{10^{2}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{3.6}} \times {\color{rgb(99,194,222)} \cancel{10^{2}}}} = \dfrac{1.0}{3.6 \times 10^{2}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.0}{3.6 \times 10^{2}}\)
Rewrite equation
\(\dfrac{1.0}{10^{2}}\text{ can be rewritten to }10^{-2}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-2}}{3.6}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0027777778\approx2.7778 \times 10^{-3}\)
\(\text{Conversion Equation}\)
\(1.0\left(EMU \text{ } of \text{ } charge\right)\approx{\color{rgb(20,165,174)} 2.7778 \times 10^{-3}}\left(ampere \times hour\right)\)
