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1.Units, Dimensions and Measurement
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What is the dimensions of impedance?
A$M{L^2}{T^{ - 3}}{I^{ - 2}}$
B${M^{ - 1}}{L^{ - 2}}{T^3}{I^2}$
C$M{L^3}{T^{ - 3}}{I^{ - 2}}$
D${M^{ - 1}}{L^{ - 3}}{T^3}{I^2}$
(AIIMS-2007)
Solution
$\begin{array}{l}
impedance\,is\,same\,as\,{\rm{resistance}}\,but\,in\,ac\,circuit\\
\therefore \,Dimension\,of\,impedance\\
= \frac{{dimension\,of\,voltage}}{{dimension\,of\,current\,}}\\
\frac{{\left[ V \right]}}{{\left[ T \right]}} = \frac{{\left[ {M{L^2}{T^{ – 3}}{I^{ – 1}}} \right]}}{I} = \left[ {M{L^2}{T^{ – 3}}{I^{ – 2}}} \right]
\end{array}$
impedance\,is\,same\,as\,{\rm{resistance}}\,but\,in\,ac\,circuit\\
\therefore \,Dimension\,of\,impedance\\
= \frac{{dimension\,of\,voltage}}{{dimension\,of\,current\,}}\\
\frac{{\left[ V \right]}}{{\left[ T \right]}} = \frac{{\left[ {M{L^2}{T^{ – 3}}{I^{ – 1}}} \right]}}{I} = \left[ {M{L^2}{T^{ – 3}}{I^{ – 2}}} \right]
\end{array}$
Standard 11
Physics
