MHT CET202527 Apr 2025Evening ShiftPhysicsAlternating CurrentActual
A resistor of 100 , inductor of self inductance ( 4 ^2 ) H and a capacitor of unknown capacitance are connected in series to an a.c. source of 200 ~V , 50 ~Hz supply. When the current and voltage are in phase, the capacitance and the power dissipated is respectively
Options
- A2 10⁻⁵ ~F , 200 ~V
- B3 10⁻⁵, 300 ~V
- C4 10⁻⁵ ~F , 400 ~W
- D2.5 10⁻⁵ ~F , 400 ~W
Correct answer
A. 2 10⁻⁵ ~F , 200 ~V
Step-by-step solution
At resonance in an RLC series circuit, the inductive and capacitive reactances are equal: X_L = X_C . The inductive reactance is calculated as X_L = 2 f L = 2 (50) ( 4 ^2 ) = 400 . The resonance condition yields 400 = 1 2 f C , leading to C = 1 100 400 = 2.5 10⁻⁵ F . At resonance, the impedance equals the resistance R = 100 , so the RMS current is I_ rms = 200 100 = 2 A and the power dissipated is P = I_ rms ^2 R = 4 100 = 400 W . The capacitance 2.5 10⁻⁵ F and power 400 W correspond to option D .