Ac Circuits

Reactance of inductor: RMS current:

A bolometer is an instrument used for measuring the power of incident electromagnetic radiation. It is commonly used to detect infrared radiation. When infrared radiation strikes the bolometer, the material in the bolometer absorbs it and experiences a change in temperature. This change in temperature leads to a change in resistance, which is then measured and can be correlated to the power of the radiation. Therefore, the correct answer is bolometer.

Given that when:
- Capacitor is removed, the circuit is RL with current lagging by
- Inductor is removed, the circuit is RC with current leading by
This means in the full LCR circuit, the phase difference is zero — i.e., resonance, so power is maximized.
Peak voltage
So RMS voltage
Resistance
Power dissipated:

The reactance of a capacitor is given by: and the reactance of an inductor is given by: where: - , - . Since , equating both reactances: Solving for : Substitute the values of and : Thus, the required frequency is .

The quality factor in a series RLC circuit is a measure of the sharpness of resonance and energy efficiency. It is given by: We derived this by substituting the resonance angular frequency into the formula. Therefore, the correct expression is .

The impedance of an RLC circuit is minimum when the frequency is such that the inductive reactance equals the capacitive reactance. From the given values, we calculate the frequency for which the impedance is minimized to be 10 kHz. Thus, the correct answer is option (2).

The power factor in an ac circuit is defined as the ratio of the resistance to the impedance , that is, For the LR circuit: - The impedance is given by , - The power factor is . For the LCR circuit: - The impedance is given by , - The power factor is . Thus, the ratio of the power factors is . Hence, the correct answer is .

Let’s break this down step by step to calculate the time lag between voltage and current in the LR circuit and determine why option (3) is the correct answer.
Step 1: Understand the concept of time lag in an LR circuit
In an LR circuit with an AC source, the voltage leads the current by a phase angle , where:

• is the inductive reactance,
• is the resistance.

The time lag between voltage and current is related to the phase angle by:

where is the angular frequency, and is the frequency of the AC source.
Step 2: Identify the given values and calculate the phase angle

• Inductive reactance,
• Resistance,
• Frequency,

Step 3: Calculate the angular frequency and time lag


Step 4: Confirm the correct answer
The calculated time lag is , which matches option (3).
Thus, the correct answer is (3) s.

At resonance in an RLC series circuit, the inductive reactance equals the capacitive reactance , so .
The impedance of the circuit is then purely resistive: .
Given: .
Thus, at resonance, .

Capacitive reactance is given by: Substitute values: