Question
Explain the term inductive reactance. Show graphically variation of inductive reactance with the frequency of the applied alternating emf.
✓
Answer
When an alternating emf e $=e_0 \sin \omega t$ is applied to a pure inductor of inductance $L$, the current in the
circuit is $i = i _0 \sin \left(\omega t -\frac{\pi}{2}\right)$, where $i _0=\frac{\pi}{2}$, where $i _0=\frac{e_0}{\omega L} \ln$ the case of a pure resistor of resistance $R_r i=i_0 \sin \omega t$ for $e=e_0 \sin \omega t$, and $i_0=\frac{e_0}{R}$
Comparison of Eqs. $i_0=\frac{e_0}{\omega L}$ and $i_0=\frac{e_0}{R}$ shows that $\omega L$ is the resistance offered by the inductor to the applied alternating emf. It is called the reactance. It increases linearly with the frequency because $\omega L =2 \pi fL$. This is illustrated in the following figure, $\omega L$ is denoted by $X_{ L }$.
circuit is $i = i _0 \sin \left(\omega t -\frac{\pi}{2}\right)$, where $i _0=\frac{\pi}{2}$, where $i _0=\frac{e_0}{\omega L} \ln$ the case of a pure resistor of resistance $R_r i=i_0 \sin \omega t$ for $e=e_0 \sin \omega t$, and $i_0=\frac{e_0}{R}$
Comparison of Eqs. $i_0=\frac{e_0}{\omega L}$ and $i_0=\frac{e_0}{R}$ shows that $\omega L$ is the resistance offered by the inductor to the applied alternating emf. It is called the reactance. It increases linearly with the frequency because $\omega L =2 \pi fL$. This is illustrated in the following figure, $\omega L$ is denoted by $X_{ L }$.
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