JEE

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The capacitive reactance is equal to the inductive reactance at resonance:

$X_L=X_C??=\frac{1}{\sqrt{L?C}}$

In an AC circuit, the power factor cos? measures the efficiency of power usage. Between the current and voltage, it is the cosine of the phase angle. A power factor of 1 means all the supplied power is used effectively and a low power factor means more energy is wasted.

Average power:

$P=V_{\text{rms}}\cdot I_{\text{rms}}\cdot cos??$

The alternating current's RMS (Root Mean Square) value or voltage offers the equivalent DC value that would generate the same power in a resistive circuit. The RMS is used in most practical measurements and is calculated as:

$I_{\text{rms}}=\frac{I_0}{\sqrt{2}},V_{\text{rms}}=\frac{V_0}{\sqrt{2}}$

Where ?0 and ?0 are the peak current and voltage, respectively.

Students can expect conceptual questions on Faraday's and Lenz's Laws, derivations involving EMF, flux calculations, and application-based questions like the functioning of generators or transformers. Numerical problems involving   and time-varying magnetic fields are also frequently included.

Lenz's law is used for devices like eddy current brakes, induction cooktops, and metal detectors. For example in induction cooktops, the currents in the cookware are induced by the changing magnetic fields. It generates the heat due to resistance. It is based on Lenz's law which follows the opposing nature of the induced current.

The negative sign in Faraday's Law of Electromagnetic Induction is extremely significant as it gives the direction of the induced EMF. Faraday's law is based on Lenz's law which reflects the principle of conservation of energy. It says that the induced EMF always opposes the magnetic flux changes that cause it. Following is the Faraday's law equation: