At time t =0 , terminal A in circuit shown in figure is connected to B by a key and alternating curr

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7.Alternating Current

normal

At time $t =0$, terminal $A$ in the circuit shown in the figure is connected to $B$ by a key and alternating current $I ( t )= I _0 \cos (\omega t$,$) , with I _0=1 A$ and $\omega=500 \ rad s ^{-1}$ starts flowing in it with the initial direction shown in the figure.

At $t=\frac{7 \pi}{6 \omega}$, the key is switched from $B$ to $D$. Now onwards on ly $A$ and $D$ are connected. $A$ total charge $Q$ flows from the battery to charge the capacitor fully. If $C =20 \mu, R =10 \Omega$ and the battery is ideal with emf of $50 \ V$, identify the correct statement $(s)$

$(A)$ Magnitude of the maximum charge on the capacitor before $t=\frac{7 \pi}{6 \omega}$ is $1 \times 10^{-3} C$.

$(B)$ The current in the left part of the circuit just before $t=\frac{7 \pi}{6 \omega}$ is clockwise

$(C)$ Immediately after $A$ is connected to $D$. the current in $R$ is $10 A$.

$(D)$ $Q =2 \times 10^{-3} C$.

$(B,C)$

$(B,D)$

$(C,D)$

$(A,D)$

(IIT-2014)

Solution

Charge on capacitor will be maximum at $t =\frac{\pi}{2 \omega}$

$Q _{\max }=2 \times 10^{-3} C$

$(A)$ charge supplied by source from $t=0$ to $t=\frac{7 \pi}{6 \omega}$

$Q=\int_0^{\frac{7 \pi}{6 \omega}} \cos (500 t) d t=\left[\frac{\sin 500 t}{500}\right]_0^{\frac{7 \pi}{6 \omega}}=\frac{\sin \frac{7 \pi}{6}}{500}=-1 m C$

$Image$

Apply KVL just after switching

$50+\frac{ Q _1}{ C }- IR =0 \Rightarrow I =10 A$

In steady state $Q_2=1 mC$ net charge flown from battery $=2 mC$

Standard 12

Physics

A resistor of $200 \;\Omega$ and a capacitor of $15.0 \;\mu \,F$ are connected in series to a $220\; V , 50\; Hz$ $ac$ source.

$(a)$ Calculate the current in the circuit;

$(b)$ Calculate the voltage $(rms)$ across the resistor and the capacitor. Is the algebraic sum of these voltages more than the source voltage? If yes, resolve the paradox.

medium

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

medium

(AIIMS-2018)

A circuit connected to an $ac$ source of $emf$ $e = e_0\, sin\, (1000t)$ with $t$ in seconds, gives a phase difference of $\frac{\pi }{4}$ between the $emf$ $e$ and current $i$. Which of the following circuits will exhibit this?

hard

(JEE MAIN-2019)

Two resistors of $10\, \Omega$ and $20\, \Omega$ and an ideal inductor of $10\, H$ are connected to a $2\, V$ battery as shown. The key $K$ is inserted at time $t = 0$. The initial $(t = 0)$ and final ($t \rightarrow \infty$ ) currents through battery are

medium

A coil of self-inductance $L$ is connected in series with a bulb $B$ and an $AC$ source. Brightness of the bulb decreases when

medium

(AIPMT-2013)

Solution

Similar Questions

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

A circuit connected to an $ac$ source of $emf$ $e = e_0\, sin\, (1000t)$ with $t$ in seconds, gives a phase difference of $\frac{\pi }{4}$ between the $emf$ $e$ and current $i$. Which of the following circuits will exhibit this?

Two resistors of $10\, \Omega$ and $20\, \Omega$ and an ideal inductor of $10\, H$ are connected to a $2\, V$ battery as shown. The key $K$ is inserted at time $t = 0$. The initial $(t = 0)$ and final ($t \rightarrow \infty$ ) currents through battery are

A coil of self-inductance $L$ is connected in series with a bulb $B$ and an $AC$ source. Brightness of the bulb decreases when

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