Lcr Circuit

Step 1: Concept
Resonance occurs when inductive reactance ( ) equals capacitive reactance ( ).
Step 2: Analysis
At resonance, the net reactance is zero, making the circuit purely resistive.
Step 3: Conclusion
In a purely resistive circuit, current and voltage are in phase, so the phase difference is zero.
Final Answer: (C)

Step 1: Period Trend
Ionization energy generally increases from left to right across a period due to increasing nuclear charge.
Step 2: Exception
Nitrogen ( ) has a half-filled subshell, which is exceptionally stable.
Step 3: Comparison
Because of this stability, it is harder to remove an electron from N than from O ( ).
Step 4: Final Order
The order is .
Final Answer: (d)

Step 1: Understand the RL circuit time constant.
For an RL circuit, the current as a function of time is given by: where is the time constant, is the inductance, and is the resistance.

Step 2: Calculate the time constant.
Given and , the time constant is:

Step 3: Time for current to reach of its maximum value.
At , the current reaches of its maximum value, so the time required is .

Step 4: Conclusion.
The time required for the current to reach of its maximum value is 2 seconds, which is option (2).

Step 1: Power formula for an AC circuit.
The average power in an AC circuit is given by: where is the maximum voltage, is the maximum current, and is the phase difference between voltage and current.

Step 2: Determine the maximum values and phase difference.
From the given equations: - , so . - , so . The phase difference .

Step 3: Calculate the power.
Now, using the formula: Since :

Step 1: Understand the relationship between current, voltage, and capacitance in an AC circuit.
The current in a capacitor connected to an AC source is given by: where is the capacitance and is the voltage.

Step 2: Differentiate the voltage.
The derivative of the voltage is: Thus, the current is:

Step 3: Conclusion.
The ammeter reads 20 mA, which is option (2).

Step 1: Understand the formula for AC time.
In an AC circuit, the time taken for the voltage to reach its maximum value is a fraction of the period of the wave. The time period for an AC with frequency is given by:

Step 2: Apply the given frequency.
We are given the frequency , so the time period is:

Step 3: Calculate the time to reach maximum value.
The time taken for the voltage to reach its maximum value is a quarter of the time period:

Step 1: Understanding the Concept:
Angular momentum is conserved when no external torque acts. .
Step 2: Detailed Explanation:
When man walks from edge to centre, moment of inertia decreases (mass moves closer to axis).
Since is constant, if decreases, must increase.
Step 3: Final Answer:
Thus, angular velocity increases.

Step 1: Understanding the Concept:
Moseley's law for line: or .
Step 2: Detailed Explanation:
.
For : .
For : .
.
Thus, .
Step 3: Final Answer:
Thus, wavelength = .

Step 1: Understanding the Concept:
Atwood machine with pulley accelerating upward. Effective acceleration due to gravity becomes where is upward acceleration.
Step 2: Detailed Explanation:
Pulley acceleration = upward. Effective .
In Atwood machine: tension .
, .
.
Step 3: Final Answer:
Thus, tension = .

Step 1: Understanding the Concept:
Relative velocity = velocity of bullet relative to ground minus velocity of thief.
Step 2: Detailed Explanation:
Police speed = 45 km/h = m/s.
Thief speed = 153 km/h = m/s.
Muzzle velocity is relative to police jeep. Bullet velocity relative to ground = m/s (same direction).
Relative velocity of bullet wrt thief = m/s.
Step 3: Final Answer:
Thus, striking velocity = 150 m/s.

Step 1: Understanding the Concept:
Time constant of an L-R circuit: time for current to reach about 63% of final value.
Step 2: Detailed Explanation:
Current growth equation: . For exponent to be dimensionless: . Hence, has dimensions of time .
Step 3: Final Answer:

Concept:
•DC: Solenoid acts as pure resistor
•AC: Impedance
•

Step 1:Find resistance:

Step 2:Find impedance:

Step 3:Using :

Step 4:Find inductance: