1. ⇒ (MHT CET 2023 12th May Evening Shift )

Resistor of $2 Ω$ , inductor of $100 μ H$ and capacitor of $400 pF$ are connected in series across a source of $e_{rms} = 0.1$ Volt. At resonance, voltage drop across inductor is

A. 25 V

B. 2.5 V

C. 250 V

D. 20 V

Correct Option is (A)

At resonance condition, $X_{C} = X_{L}$

The impedance is given as:

$\begin{aligned} Z & = \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}} \\ ∴ Z & = R = 2 Ω \\ I_{rms} & = \frac{e_{ms}}{R} \\ I_{rms} & = \frac{0.1}{2} = 0.05 A \\ ω & = \frac{1}{\sqrt{LC}} = \frac{1}{\sqrt{10^{- 4} \times 4 \times 10^{- 10}}} \\ ω & = 5 \times 10^{6} \end{aligned}$

$∴$ The voltage-drop across the inductor is,

$\begin{aligned} V = I_{rms} \times X_{L} = I_{rms} \times L ω \\ V = 0.05 \times 10^{- 4} \times 5 \times 10^{6} \\ V = 25 V \end{aligned}$

2. ⇒ (MHT CET 2023 11th May Evening Shift )

In a series LCR circuit, $C = 2 μ F, L = 1 mH$ and $R = 10 Ω$ . The ratio of the energies stored in the inductor and the capacitor, when the maximum current flows in the circuit, is

A. $5 : 1$

B. $3 : 2$

C. $1 : 2$

D. $1 : 5$

Correct Option is (A)

In resonance condition (current is maximum),

$∴ X_{C} = X_{L}$

$∴$ The ratio of energies in the inductor and capacitor is:

$\begin{aligned} \frac{U_{L}}{U_{C}} = \frac{{LI}^{2}}{{CV}^{2}} = \frac{L}{{CR}^{2}} \dots . (∵ \frac{I}{V} = \frac{1}{R}) \\ \frac{U_{L}}{U_{C}} = \frac{10^{- 3}}{2 \times 10^{- 6} \times 10^{2}} \\ \frac{U_{L}}{U_{C}} = \frac{5}{1} \end{aligned}$

3. ⇒ (MHT CET 2023 10th May Morning Shift )

In the circuit shown the ratio of quality factor and the bandwidth is

MHT CET 2023 10th May Morning Shift Physics - Alternating Current Question 19 English

A. 10 s

B. 8 s

C. 6 s

D. 4 s

Correct Option is (A)

$\begin{aligned} Bandwidth = 2 Δ ω = \frac{R}{L} \\ Q factor = \frac{1}{R} \sqrt{\frac{L}{C}} \\ \frac{Q factor}{Band width} = \frac{\frac{1}{R} \sqrt{\frac{L}{C}}}{\frac{R}{L}} = \frac{1}{R^{2}} \frac{L^{3 / 2}}{\sqrt{C}} \\ \frac{Q_{factor}}{Bandwidth} = \frac{3 \sqrt{3}}{100 \sqrt{27 \times 10^{- 6}}} = \frac{3 \sqrt{3}}{100 \times 3 \sqrt{3} \times 10^{- 3}} = 10 s \end{aligned}$

4. ⇒ (MHT CET 2023 9th May Evening Shift )

An alternating voltage of frequency ' $ω$ ' is induced in electric circuit consisting of an inductance ' $L$ ' and capacitance ' $C$ ', connected in parallel. Then across the inductance coil

A. current is maximum when $ω^{2} = \frac{1}{LC}$

B. current is zero

C. voltage is minimum when $ω^{2} = \frac{1}{LC}$

D. voltage is maximum when $ω^{2} = \frac{1}{LC}$

Correct Option is (D)

In a parallel $LC$ circuit at $ω^{2} = \frac{1}{LC}$ , the current is minimum.

As current and voltage are out of phase by $90^{\circ}$ , the voltage would be maximum.

5. ⇒ (MHT CET 2021 21th September Evening Shift )

In LCR series resonant circuit, at resonance, voltage across 'L' and 'C' will cancel each other because they are

A. 90 $^{\circ}$ out of phase

B. 90 $^{\circ}$ in phase

C. 180 $^{\circ}$ in phase

D. 180 $^{\circ}$ out of phase

Correct Option is (D)

Currently no explanation available

⇒AC Circuits