KVPY 2016 Q98. Chapter - Alternating Current , the answer is C which my teacher told but his way was not at all logical i think , can anyone please send me a proper solution to this question.

To tackle KVPY 2016 Question 98 from the chapter on Alternating Current, let’s break down the problem step by step. The question likely revolves around concepts such as impedance, phase difference, or power in AC circuits. While I don’t have the exact wording of the question, I can guide you through a logical approach to similar problems in this topic.

Understanding the Basics of AC Circuits

Alternating Current (AC) circuits have unique characteristics compared to Direct Current (DC) circuits. In AC circuits, the current and voltage vary sinusoidally with time. Key concepts include:

• Impedance (Z): This is the total opposition to current flow in an AC circuit, combining resistance (R) and reactance (X).
• Phase Difference: This refers to the difference in phase angle between the voltage and current waveforms.
• Power Factor: This is the cosine of the phase angle and indicates how effectively the current is being converted into useful work.

Analyzing the Problem

Let’s assume the question involves calculating the impedance in a circuit with a resistor and an inductor or capacitor. The impedance can be calculated using the formula:

Z = √(R² + X²)

Where:

• R: Resistance in ohms (Ω)
• X: Reactance in ohms (Ω), which can be inductive (XL = ωL) or capacitive (XC = 1/ωC).

Example Scenario

Imagine you have a circuit with a resistor of 4Ω and an inductor with a reactance of 3Ω. The impedance would be calculated as follows:

Z = √(4² + 3²) = √(16 + 9) = √25 = 5Ω

This means the total opposition to the current in this circuit is 5Ω. If the question asks for the phase angle (φ), you can find it using:

tan(φ) = X/R

In our example:

tan(φ) = 3/4

To find φ, you would take the arctan of 3/4, which gives you the phase difference between the voltage and current.

Power Calculation

If the question involves power, the real power (P) in an AC circuit can be calculated using:

P = VI cos(φ)

Where:

• V: Voltage across the circuit
• I: Current through the circuit

By substituting the known values, you can determine the power consumed by the circuit.

Final Thoughts

In summary, when approaching questions related to AC circuits, focus on understanding the relationships between resistance, reactance, impedance, and phase angle. Each component plays a crucial role in determining the overall behavior of the circuit. If you can provide the specific details of the question, I can offer a more tailored solution. However, the logical steps outlined here should help you navigate similar problems effectively.