Ac Circuits

Step 1: Understanding the resonant frequency of LCR circuit.
The resonant frequency of an LCR circuit is given by: Step 2: Finding the new capacitance for the same frequency.
When the inductance is changed to , for the frequency to remain the same, the capacitance must change such that: Solving this, we find that . Thus, the correct answer is (C) .

Step 1: Write expressions for reactances.
Inductive reactance:
Capacitive reactance:


Step 2: At resonance.
At frequency :


Step 3: Change frequency to .


Step 4: Find relation.
Since :


Step 5: Conclusion.
The correct relation is .

Step 1: Understanding stress and its relation.
Stress is defined as force per unit area, , where is the force applied and is the cross-sectional area of the wire. Since wire A has twice the radius of wire B, the area of wire A is four times greater than that of wire B (because area ).
Step 2: Relating stress to the radius.
Since stress is inversely proportional to the cross-sectional area , the stress on wire B will be four times that on wire A, given that wire A has a larger area.
Step 3: Conclusion.
The stress on wire B is four times greater than on wire A, hence the correct answer is (B) four times.

Step 1: Understanding the behavior of an LC parallel resonant circuit.
In an LC parallel resonant circuit, the current reaches its maximum value when the impedance of the circuit is minimum at the resonant frequency. This occurs because the reactances of the inductor and capacitor cancel each other out, resulting in purely resistive behavior at resonance. Step 2: Graph analysis.
- Option (A): This graph shows a maximum current but does not necessarily indicate a minimum impedance. This is not a correct representation of resonance in an LC circuit. - Option (B): This graph shows a minimum current, which is incorrect for resonance. - Option (C): Correct. This graph shows maximum current and minimum impedance at the resonant frequency, which is characteristic of an LC parallel resonant circuit. - Option (D): This graph does not show the typical behavior of current and impedance in a resonant circuit. Step 3: Conclusion.
Thus, the correct answer is (C), which correctly shows maximum current and minimum impedance at resonance.

Step 1: Understanding the LCR circuit.
In a series LCR circuit, the total impedance is given by: Where: - - - Substituting the values into the equation: Step 2: Calculating the impedance.
Now, calculate the total impedance : Step 3: Calculating the peak current.
The peak current is given by: Where . Substituting the values: Thus, the correct answer is (B) 0.20 A.

Step 1: Understanding the resonance condition.
In a parallel resonant circuit, the current in the main circuit is zero at resonance, because the currents through the inductor and capacitor are equal and opposite. Therefore, , and the net current is zero.

Step 2: Analyzing the options.
- (A) is correct because at resonance, the inductor and capacitor currents cancel each other out, but are equal in magnitude. - (B) is incorrect because at resonance, there is no net current, and both inductor and capacitor have non-zero currents. - (C) is incorrect because at resonance. - (D) is incorrect because at resonance, .

Step 3: Conclusion.
The correct answer is (A), as it correctly describes the condition for resonance in a parallel LC circuit.

Step 1: Function of a repeater.
A repeater is an electronic device that amplifies or regenerates a signal to extend its range. It is essentially a combination of a receiver, which receives the signal, and a transmitter, which transmits the amplified signal.
Step 2: Conclusion.
The correct answer is (B). A repeater is a combination of a receiver and a transmitter.