Alternating Current

In l-C-R series circuit, resonance occurs when

or
or
or



When capacitance of the circuit is made 4 times, Iet its resonant frequency become .
or

Step 1: Ohm’s Law in AC circuits.
In AC circuits, the current is related to the EMF by the formula: where , and is the total resistance in the circuit.
Step 2: Conclusion.
For this circuit, the value of the current is given by , which corresponds to option (A).

Step 1: Resonance condition in an LCR circuit.
In an LCR circuit, resonance occurs when the reactance of the inductor equals the reactance of the capacitor. At resonance, the impedance of the circuit is minimized, and the current reaches its maximum.
Step 2: Conclusion.
The resonance condition in this circuit corresponds to , so the correct answer is (C).

Step 1: Phase difference in AC circuits.
The phase difference in an AC circuit with an inductor, capacitor, and resistor depends on the impedance of the circuit. In a series resonance circuit, the phase difference is minimized, and the current is in phase with the applied voltage.
Step 2: Conclusion.
For the coil connected to an AC circuit, the phase difference will be minimized in an LCR series resonance, so the correct answer is (B).

Step 1: Understanding the Concept:
For an ideal transformer, power input equals power output ( ). This leads to the relationship: .
Step 2: Detailed Explanation:
Given: , , A. $ $
Step 3: Final Answer:
The input current is 10 A.

Step 1: Understanding the Concept:
An LC circuit oscillates by transferring energy back and forth between the electric field of the capacitor and the magnetic field of the inductor. The natural angular frequency is .
Step 2: Calculation:
Given: F, H. $ $ Rounding to the nearest option: 1100 rad/s.
Step 3: Final Answer:
The angular frequency is 1100 rad/s.

Step 1: Understanding the Concept:
Capacitive reactance ( ) is the opposition offered by a capacitor to the flow of alternating current. It is inversely proportional to frequency and capacitance.
Step 2: Calculation:
Formula: Given: Hz, F. $ \Omega$.