Question

$\mathbf{1}\mathit{H}\mathbf{=}\mathbf{1}\mathit{\Omega }$and $\mathbf{\backslash (}\mathbf{1}\mathit{H}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}\mathit{W}\mathit{h}\mathbf{/}\mathit{A}\mathbf{\backslash )}$ . Show that these two definitions are equivalent.

Short answer

Answer

Yes, these definitions are equivalent. It means $1H=1\frac{Wb}{A}$.

Step-by-step solution

Definition of current

The term current may be defined as the ratio of charge and time.

Step 2:show that these definitions are equivalent

The relation between inductance and magnetic flux is$M=\frac{N{\varphi }_B}{i}$

$$\begin{gathered} 1H=\frac{1Wb}{1A} \\ 1Wb=1V.s \\ 1H=\frac{1V.s}{1A} \end{gathered}$$

Using ohm’s law

$$\begin{gathered} V=I.R \\ V=1A.\Omega \end{gathered}$$

Then

$$\begin{gathered} 1H=1\frac{A.\Omega .s}{A} \\ =1\Omega .s \end{gathered}$$

Hence,these definitions are equivalent. It means $1H=1\frac{Wb}{A}$.