In the circuit shown, , and . They are connected in series with an a.c. source as shown. Which of the following options is/are correct? [2017]

Question

In the circuit shown, $L = 1 μ H$ , $C = 1 μ F$ and $R = 1 k Ω$ . They are connected in series with an a.c. source $V = V_{0} \sin ω t$ as shown. Which of the following options is/are correct [2017]

Smart Achievers · Accepted Answer

(2, 3)

The frequency at which the current is in phase with the voltage is the resonance frequency.

$ω_{r} = \frac{1}{\sqrt{L C}} = \frac{1}{{(10^{- 6} \times 10^{- 6})}^{1 / 2}} = 10^{6} {rad s}^{- 1}$

This frequency is independent of $' R'$ .

At $ω \approx 0$ , the current is $i = \frac{V}{\sqrt{R^{2} + {(ω L - \frac{1}{ω C})}^{2}}}$

i.e., the current through the circuit nearly becomes zero.

If $ω ≫ ω_{r},$ $X_{L} > X_{C}$ so the circuit behaves like an inductor.

Solution

Q.
In the circuit shown, $L = 1 μ H$ , $C = 1 μ F$ and $R = 1 k Ω$ . They are connected in series with an a.c. source $V = V_{0} \sin ω t$ as shown. Which of the following options is/are correct [2017]

1 The current will be in phase with the voltage if $ω = 10^{4} rad s^{- 1} .$

2 The frequency at which the current will be in phase with the voltage is independent of R.

3 At $ω ~ 0$ , the current flowing through the circuit becomes nearly zero.

4 At $ω ≫ 10^{6} rad s^{- 1}$ , the circuit behaves like a capacitor.

Want Us to Email you About Special Offers & Updates?

Solution

Q. In the circuit shown, L=1 μH, C=1 μF and R=1 kΩ. They are connected in series with an a.c. source V=V0sinωt as shown. Which of the following options is/are correct [2017]

1 The current will be in phase with the voltage if ω=104rad s-1.