Power in AC — Power factor, wattless current

Q47.In a series LCR circuit, a resistor of 300Ω, a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is _____ ×104 radians s−1 .

Q28.Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury 2025 (29 Jan Shift 1) JEE Main Previous Year Paper tube, the tube will be damaged. Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor + , where ω is frequency of the supply across resistor R and inductor L . If the choke (R/√R2 ω2L2) coil were not used, the voltage across the resistor would be the same as the applied voltage. In the light of the above statements, choose the most appropriate answer from the options given below : (1) (A) is true but (R) is false (2) Both (A) and (R) are true and (R) is the correct explanation of (A) (3) (A) is false but (R) is true (4) Both (A) and (R) are true but (R) is not the correct explanation of (A)

Q39.A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is I0 . If the value of resistance R becomes twice of its initial value then amplitude of current at resonance will be (1) 2I0 (2) I0 (3) I0 (4) I0 2 √2

Q46.A time varying potential difference is applied between the plates of a parallel plate capacitor of capacitance 2.5μ F. The dielectric constant of the medium between the capacitor plates is 1 . It produces an instantaneous displacement current of 0.25 mA in the intervening space between the capacitor plates, the magnitude of the rate of change of the potential difference will be _____ Vs−1 .

Q28.An alternating current is given by I = IA sin ωt + IB cos ωt. The r.m.s current will be ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ 2025 (24 Jan Shift 1) JEE Main Previous Year Paper (1) |IA+IB| (2) A+I2B √2 √I2 2 B + I2B (4) √I2A+I2 (3) √I2A 2

Q15.In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to : A. pure inductor. B. pure capacitor. C. pure resistor. D. combination of an inductor and capacitor. Choose the correct answer from the options given below : (1) A, B and C only (2) A and B only (3) B, C and D only (4) A, B and D only →