Semiconductor Electronics Materials Devices And Simple Circuits

In this case, the circuit contains resistance , inductance , and capacitance , connected in series with an AC voltage source.
The phase difference between the voltage and the current is influenced by the presence of the inductor and capacitor.
The phase difference in an RLC circuit is given by the formula: where:
- is the inductive reactance,
- is the capacitive reactance,
- is the angular frequency of the AC voltage source. When the inductor is removed, the phase difference becomes: When the capacitor is removed, the phase difference becomes: This implies that both reactances, inductive and capacitive, are equal, and the circuit behaves as a purely resistive circuit when either component is removed.
Thus, the power factor of the circuit is: Therefore, the correct answer is:

In this circuit, the resistors are connected in a combination of series and parallel.
Let's break it down:
- Resistors between points 1 and 6 are in series, so the total resistance between points 1 and 6 will be the sum of the resistances of the two resistors connected in series:
- Resistors between points 3 and 6 are in parallel. The equivalent resistance for two resistors in parallel is given by: - The total resistance between points 2 and 4 is the parallel combination of two resistors each of resistance :
Thus, the total resistance between points 2 and 4 is .

The phase difference between the current and voltage in an RL circuit is given by: where is the inductive reactance and is the resistance.
Step 1: Finding the inductive reactance
The inductive reactance is given by: where is the frequency of the AC supply and is the inductance of the coil. Given: - , - .
Thus, the inductive reactance is:
Step 2: Calculating the phase difference
Now, we can calculate the phase difference: Taking the inverse tangent:
Hence, the phase difference is approximately , which corresponds to option (D).