MHT CET202410 May 2024Evening ShiftPhysicsAlternating CurrentActual
For the series LCR circuit, R= X_L 2 =2 X_c . The impedance of the circuit and the phase difference between V and I will be
Options
- A5 2 R , ⁻¹ ( 1 2 )
- B13 2 R, ⁻¹ ( 3 2 )
- C5 R, ⁻¹(1)
- D13 R , ⁻¹(2)
Correct answer
B. 13 2 R, ⁻¹ ( 3 2 )
Step-by-step solution
Impedance ( Z )= R ^2+ ( X _ L - X _ C )^2 ...(i) Given R= X_L 2 X_L=2 R ...(ii) Also, R =2 X _ C X _ C = R 2 ...(iii) Substituting (ii) and (iii) in (i), Z= R^2+ (2 R- R 2 )^2 = 13 4 R^2 = 13 2 R Phase difference = ⁻¹ ( X _ L - X _ C R )= ⁻¹ ( 3 2 ) Since the impedance values provided in the options are all different, calculating the impedance will be enough to identify the correct answer.