What are Inductive Reactance ($XL$) and Capacitive Reactance ($XC$)? Explain how their values depend on the frequency of the alternating current.

Q: What are Inductive Reactance ($XL$) and Capacitive Reactance ($XC$)? Explain how their values depend on the frequency of the alternating current.

Inductive Reactance ($XL$):\nInductive reactance is the opposition offered by an inductor to the flow of alternating current. It is measured in ohms ($\Omega$). Mathematically, it is given by: $$XL = \omega L = 2\pi f L$$\nwhere $L$ is the inductance and $f$ is the frequency of the AC supply. Inductive reactance is directly proportional to frequency ($XL \propto f$). For DC ($f = 0$), $XL = 0$, meaning an inductor offers zero resistance to direct current, but as frequency increases, its opposition to AC increases linearly. Capacitive Reactance ($XC$):\nCapacitive reactance is the opposition offered by a capacitor to the flow of alternating current. It is also measured in ohms ($\Omega$). Mathematically, it is given by: $$XC = \frac{1}{\omega C} = \frac{1}{2\pi f C}$$\nwhere $C$ is the capacitance and $f$ is the frequency. Capacitive reactance is inversely proportional to frequency ($XC \propto \frac{1}{f}$). For DC ($f = 0$), $XC = \infty$, which means a capacitor completely blocks direct current. However, for high-frequency AC, capacitive reactance becomes very small, allowing high-frequency current to pass easily through it.

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Inductive Reactance ($XL$):
Inductive reactance is the opposition offered by an inductor to the flow of alternating current. It is measured in ohms ($\Omega$). Mathematically, it is given by: $$XL = \omega L = 2\pi f L$$
where $L$ is the inductance and $f$ is the frequency of the AC supply. Inductive reactance is directly proportional to frequency ($XL \propto f$). For DC ($f = 0$), $XL = 0$, meaning an inductor offers zero resistance to direct current, but as frequency increases, its opposition to AC increases linearly. Capacitive Reactance ($XC$):
Capacitive reactance is the opposition offered by a capacitor to the flow of alternating current. It is also measured in ohms ($\Omega$). Mathematically, it is given by: $$XC = \frac{1}{\omega C} = \frac{1}{2\pi f C}$$
where $C$ is the capacitance and $f$ is the frequency. Capacitive reactance is inversely proportional to frequency ($XC \propto \frac{1}{f}$). For DC ($f = 0$), $XC = \infty$, which means a capacitor completely blocks direct current. However, for high-frequency AC, capacitive reactance becomes very small, allowing high-frequency current to pass easily through it.

CBSE · Class 12 · Physics · Alternating CurrentWhat are Inductive Reactance ($XL$) and Capacitive Reactance ($XC$)? Explain how their values depend on the frequency of the alternating current.