A series RLC circuit is made as shown in the figure with an AC source of 60 V, 20 Hz. Then

the rms current through the resistor R is 4.2 A

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the effective potential difference between P and Q should be 42 V.

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the instantaneous current leads the source voltage by

45^{\circ}

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the instantaneous current lags behind the applied voltage by

45^{\circ}

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Solution

The correct options are
A the rms current through the resistor R is 4.2 A
B the effective potential difference between P and Q should be 42 V.
D the instantaneous current lags behind the applied voltage by $45^{\circ}$
$Z = \sqrt{R^{2} + (X_{L} - X_{C})^{2}} = \sqrt{100 + 100} = 10 \sqrt{2} Ω$
$∴ I = \frac{60}{10 \sqrt{2}} = 6 \times 0.707 = 4.2 A$
$∴ V_{R} = 4.2 \times 10 = 42 V$
The phase difference $ϕ = t a n^{- 1} (\frac{X_{L} - X_{C}}{R}) = t a n^{- 1} 1 = 45^{\circ}$
As $X_{L} > X_{C}$ , Source voltage leads the current by $45^{\circ}$

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Similar questions

Q. A series LCR circuit with

100 Ω

resistance is connected to an AC source of

200 V

and angular frequency

300 rad/s

. When only the capacitance is removed, the current lags behind the voltage by

60^{\circ}

. When only the inductance is removed, the current leads the voltage by

60^{\circ}

. The rms current in the LCR circuit is -

An RLC circuit with $R = 100 Ω$ is connected across ac source of 200V and angular frequency 300 rad/s. When the only capacitance is removed, the current lags behind voltage by $60^{\circ}$ . When only inductance is removed, the current leads the voltage by $60^{\circ}$ . The current in the circuit is___(in Ampere)