Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsQuestion Bank [ 2022 ]3 Marks
Question
Explain the term capacitive reactance. State its unit and dimensions.
✓
Answer
i. The peak value of alternating current through a capacitor is given by, $ i _0=\frac{ e _0}{(1 / \omega C )} $ ii. For a capacitive a.c. circuit, According to Ohm's law, $ i =\frac{ V }{ R } $ where $R$ = resistance of the circuit. iii. Comparing equations ( 1 ) and (2), we conclude that $\left(\frac{1}{\omega C }\right)$ plays a similar role in capacitive $AC$ circuit as resistance in a purely resistive circuit. iv. Hence, the effective resistance $\left(X_C\right)$ offered by the capacitor $C$ is given as, $ X _{ C }=\frac{1}{\omega C }=\frac{1}{2 \pi fC } \cdots \cdots\left(\because \omega=\frac{2 \pi}{ T }=2 \pi f \right) $ Where $f=$ frequency of $A C$ supply v. The function of capacitive reactance in a purely capacitive circuit is to limit the amplitude of the current similar to the resistance in a purely resistive circuit. vi. $X_C$ varies inversely as the frequency of $A C$ and also as the capacitance of the condenser. vii. In a $D C$ circuit, $f=0$ $ \therefore X _{ C }=\infty $ Thus, the capacitor blocks DC and acts as an open circuit while it passes $A C$ of high frequency. viii. The dimensions of capacitive reactance are $\left[ ML ^2 T ^{-3}\right.$ I ${ }^{-2}$ ] and its SI unit is the ohm $(\Omega)$.
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