Quantum Mechanical Model Of Atom

Step 1: Understanding Power Factor
The power factor ( ) in an AC circuit is given by: where:
- is the resistance,
- is the impedance of the circuit.
Step 2: Condition at Resonance
- The impedance ( ) in an LCR circuit is given by: where:
- is the inductive reactance,
- is the capacitive reactance. - At resonance, , which simplifies the impedance to:
Step 3: Calculating Power Factor
Thus, the power factor of an LCR circuit at resonance is .

Step 1: Understanding the Resistance of an Ideal Ammeter
- An ammeter measures current and is connected in series with a circuit.
- For an ideal ammeter:
- It should not affect the current.
- It must have zero resistance ( ) so that it does not cause a voltage drop.
Step 2: Understanding the Resistance of an Ideal Voltmeter
- A voltmeter measures voltage and is connected in parallel with a circuit.
- For an ideal voltmeter:
- It should not draw any current from the circuit.
- It must have infinite resistance ( ) so that it does not disturb the circuit. Thus, the resistances of an ideal ammeter and voltmeter are and respectively.

Step 1: Understanding Magnetic Intensity ( )
Magnetic intensity ( ) in a solenoid is given by the formula: where:
is the number of turns per meter,
is the current in amperes.
Step 2: Substituting the given values
Given: Calculating:
Step 3: Effect of Relative Permeability
The presence of a material with relative permeability ( ) modifies the magnetic field.
The permeability factor is given as:
Given , we calculate: .Thus, the final value of magnetic intensity is .