A circuit with an electrical load having impedance $Z$ is connected with an AC source as shown in the diagram. The source voltage varies in time as $V(t)=300 \sin (400 t) \mathrm{V}$, where $t$ is time in s . List-I shows various options for the load. The possible currents $i(t)$ in the circuit as a function of time are given in List-II.
Choose the option that describes the correct match between the entries in List-I to those in ListII.
| List–I | List–II |
|---|---|
(P)  |
(1)  |
(Q)  |
(2)  |
(R)  |
(3)  |
(S)  |
(4)  |
(5)  |
The circuit shown in the figure contains an inductor $L$, a capacitor $C_0$, a resistor $R_0$ and an ideal battery. The circuit also contains two keys $\mathrm{K}_1$ and $\mathrm{K}_2$. Initially, both the keys are open and there is no charge on the capacitor. At an instant, key $\mathrm{K}_1$ is closed and immediately after this the current in $R_0$ is found to be $I_1$. After a long time, the current attains a steady state value $I_2$. Thereafter, $\mathrm{K}_2$ is closed and simultaneously $\mathrm{K}_1$ is opened and the voltage across $C_0$ oscillates with amplitude $V_0$ and angular frequency $\omega_0$.
Match the quantities mentioned in List-I with their values in List-II and choose the correct option.
| List-I | List-II |
|---|---|
| (P) The value of $I_1$ in Ampere is | (1) $0$ |
| (Q) The value of $I_2$ in Ampere is | (2) $2$ |
| (R) The value of $\omega_0$ in kilo-radians/s is | (3) $4$ |
| (S) The value of $V_0$ in Volt is | (4) $20$ |
| (5) $200$ |
| List - I | List - II |
|---|---|
| (P) $I_0$ in $\mathrm{mA}$ | (1) 44.4 |
| (Q) The quality factor of the circuit | (2) 18 |
| (R) The bandwidth of the circuit in $\mathrm{rad}~ \mathrm{s}^{-1}$ | (3) 400 |
| (S) The peak power dissipated at resonance in Watt | (4) 2250 |
| (5) 500 |
In the method using the transformers, assume that the ratio of the number of turns in the primary to that in the secondary in the step-up transformer is 1 : 10. If the power of the consumers has to be supplied at 200 V, the ratio of the number of turns in the primary to that in the secondary in the step-down transformer is
You are given many resistances, capacitors and inductors. These are connected to a variable DC voltage source (the first two circuits) or an AC voltage source of 50 Hz frequency (the next three circuits) in different ways as shown in Column II. When a current I (steady state for DC or rms for AC) flows through the circuit, the corresponding voltage $V_1$ and $V_2$ (indicated in circuits) are related as shown in Column I. Match the two :
An AC voltage source of variable angular frequency $$\omega$$ and fixed amplitude V0 is connected in series with a capacitance C and an electric bulb of resistance R (inductance zero). When $$\omega$$ is increased
STATEMENT 1
A vertical iron rod has a coil of wire wound over it at the bottom end. An alternating current flows in the coil. The rod goes through a conducting ring as shown in the figure. The ring can float at a certain height above the coil.
Because
STATEMENT 2
In the above situation, a current is induced in the ring which interacts with the horizontal component of the magnetic field to produce an average force in the upward direction.
The value of C is ____________.
The value of $$\varphi$$ is ____________.
A series RC combination is connected to an AC voltage of angular frequency $$\omega$$ = 500 rad/s. If the impedance of the RC circuit is R$$\sqrt{1.25}$$, the time constant (in millisecond) of the circuit is __________.
$${V_x} = {V_0}\,\sin \,\omega t,$$
$${V_Y} = {V_0}\,\sin $$ $$\left( {\omega t + {{2\pi } \over 3}} \right)$$
and $$Vz = {V_0}\sin \left( {\omega t + {{4\pi } \over 3}} \right)$$
An ideal voltmeter is configured to read $$rms$$ value of the potential difference between its terminals. It is connected between points $$X$$ and $$Y$$ and then between $$Y$$ and $$Z.$$ The reading(s) of the voltmeter will be
Which of the following options is/are correct?
In the given circuit, the AC source has $$\omega$$ = 100 rad/s. Considering the inductor and capacitor to be ideal, the correct choice(s) is(are)
A series RC-current is connected to AC voltage source. Consider two cases : (A) When C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current IR through the resistor and voltage VC across the capacitor are compared in the two cases. Which of the following is/are true?