Which of the following units denotes the dime | vedclass

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(C) The dimensional formula for inductance $L$ is given by $L = \frac{\phi}{I}$,where $\phi$ is magnetic flux and $I$ is current.Since $\phi = B \cdot

Vedclass · Accepted Answer

$Henry$ $(H)$

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(C) The dimensional formula for inductance $L$ is given by $L = \frac{\phi}{I}$,where $\phi$ is magnetic flux and $I$ is current.Since $\phi = B \cdot A$,the dimensions of flux are $[M L^2 T^{-2} A^{-1}]$.Using $Q = I \cdot T$,we have $A = Q T^{-1}$.Substituting these into the formula for inductance:$[L] = \frac{[M L^2 T^{-2} (Q T^{-1})^{-1}]}{[Q T^{-1}]} = \frac{[M L^2 T^{-2} Q^{-1} T]}{[Q T^{-1}]} = \frac{[M L^2 T^{-1} Q^{-1}]}{[Q T^{-1}]} = M L^2 Q^{-2}$.Thus,the dimensions $\frac{M L^2}{Q^2}$ correspond to the unit of inductance,which is $Henry$ $(H)$.

Which of the following units denotes the dimensions $\frac{M L^2}{Q^2}$,where $Q$ denotes the electric charge?

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