JEE Main Alternating Current PYQ

31. (JEE Main 2018 (Offline))

For an RLC circuit driven with voltage of amplitude vm and frequency $ω_{0}$ = $\frac{1}{\sqrt{L C}}$ the current exhibits resonance. The quality factor, Q is given by :

A. $\frac{C R}{ω_{0}}$

B. $\frac{ω_{0} L}{R}$

C. $\frac{ω_{0} R}{L}$

D. $\frac{R}{(ω_{0} C)}$

Correct Option is (B)

Quality factor (Q) = $\frac{A n g u l a r Re s o n a n c e}{B a n d w i t h}$

= $\frac{\frac{1}{\sqrt{L C}}}{\frac{R}{L}}$

= $\frac{ω_{0}}{\frac{R}{L}}$

= $\frac{ω_{0} L}{R}$

32. (AIEEE 2006)

In a series resonant $L C R$ circuit, the voltage across $R$ is $100$ volts and $R = 1 k Ω$ with $C = 2 μ F .$ The resonant frequency $ω$ is $200$ $r a d / s$ . At resonance the voltage across $L$ is

A. $2.5 \times 10^{- 2} V$

B. $40$ $V$

C. $250$ $V$

D. $4 \times 10^{- 3} V$

Correct Option is (C)

Across resistor, $I = \frac{V}{R} = \frac{100}{1000} = 0.1 A$

At resonance,

$X_{L} = X_{C} = \frac{1}{ω C}$

$= \frac{1}{200 \times 2 \times 10^{- 6}} = 2500$

Voltage across $L$ is

$I X_{L} = 0.1 \times 2500 = 250 V$

33. (AIEEE 2004)

In a $L C R$ circuit capacitance is changed from $C$ to $2$ $C$ . For the resonant frequency to remain unchaged, the inductance should be changed from $L$ to

A. L/2

B. 2L

C. 4L

D. L/4

Correct Option is (A)

For resonant frequency to remain same $L C$ should be const. $L C =$ const

$\Rightarrow L C = L^{'} \times 2 C \Rightarrow L^{'} = \frac{L}{2}$

34. ( AIEEE 2002)

The power factor of $A C$ circuit having resistance $(R)$ and inductance $(L)$ connected in series and an angular velocity $ω$ is

A. $R / ω L$

B. $R / {(R^{2} + ω^{2} L^{2})}^{1 / 2}$

C. $ω L / R$

D. $R / {(R^{2} - ω^{2} L^{2})}^{1 / 2}$

Correct Option is (B)

The impedance triangle for resistance $(R)$ and inductor $(L)$ connected in series is shown in the figure.

AIEEE 2002 Physics - Alternating Current Question 106 English Explanation

Power factor $\cos ϕ = \frac{R}{\sqrt{R^{2} + ω^{2} L^{2}}}$