(A) For a series $R-C$ circuit,the total applied voltage $V$ is given by the phasor sum of the voltage across the resistor $V_R$ and the voltage acros

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$6\, V, \tan^{-1}\left(\frac{4}{3}\right)$

(A) For a series $R-C$ circuit,the total applied voltage $V$ is given by the phasor sum of the voltage across the resistor $V_R$ and the voltage across the capacitor $V_C$:$V^2 = V_R^2 + V_C^2$Given $V = 10\, V$ and $V_C = 8\, V$,we have:$10^2 = V_R^2 + 8^2$$100 = V_R^2 + 64$$V_R^2 = 100 - 64 = 36$$V_R = 6\, V$Now,the phase difference $\phi$ between the current and the applied voltage is given by:$\tan \phi = \frac{V_C}{V_R}$$\tan \phi = \frac{8}{6} = \frac{4}{3}$$\phi = \tan^{-1}\left(\frac{4}{3}\right)$Thus,the voltage across $R$ is $6\, V$ and the phase difference is $\tan^{-1}\left(\frac{4}{3}\right)$.

Class 12 Physics Alternating Current RL, RC and LC AC Circuits

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In a series $R-C$ circuit shown in the figure,the applied voltage is $10\, V$ and the voltage across the capacitor is found to be $8\, V$. Then,the voltage across $R$ and the phase difference between the current and the applied voltage will respectively be

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A
$6\, V, \tan^{-1}\left(\frac{4}{3}\right)$
B
$3\, V, \tan^{-1}\left(\frac{3}{4}\right)$
C
$6\, V, \tan^{-1}\left(\frac{5}{3}\right)$
D
None of these

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$A$ coil of inductance $0.50 \; H$ and resistance $100 \; \Omega$ is connected to a $240 \; V, 50 \; Hz$ $AC$ supply.
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$(b)$ What is the time lag between the voltage maximum and the current maximum?

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Medium

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MediumJEE MAIN 2021

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$A$ sinusoidal voltage of peak value $283 \, V$ and angular frequency $320 \, rad/s$ is applied to a series $LCR$ circuit. Given that $R = 5 \, \Omega$,$L = 25 \, mH$,and $C = 1000 \, \mu F$. The total impedance and the phase difference between the voltage across the source and the current will respectively be:

DifficultJEE MAIN 2017

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In a series $R-C$ circuit shown in the figure,the applied voltage is $10\, V$ and the voltage across the capacitor is found to be $8\, V$. Then,the voltage across $R$ and the phase difference between the current and the applied voltage will respectively be

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$A$ coil of inductance $0.50 \; H$ and resistance $100 \; \Omega$ is connected to a $240 \; V, 50 \; Hz$ $AC$ supply.$(a)$ What is the maximum current in the coil?$(b)$ What is the time lag between the voltage maximum and the current maximum?

An alternating voltage is applied to a series $LCR$ circuit. If the current leads the voltage by $45^{\circ}$,then $\left(\tan 45^{\circ}=1\right)$:

An $AC$ circuit has an inductor and a resistor of resistance $R$ in series,such that $X_L = 3R$. Now,a capacitor is added in series such that $X_C = 2R$. The ratio of the new power factor to the old power factor of the circuit is $\sqrt{5} : x$. The value of $x$ is ...... .

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$A$ coil of inductance $0.50 \; H$ and resistance $100 \; \Omega$ is connected to a $240 \; V, 50 \; Hz$ $AC$ supply.
$(a)$ What is the maximum current in the coil?
$(b)$ What is the time lag between the voltage maximum and the current maximum?