The peak voltage in a $220 \mathrm{V}$,$50 \mathrm{Hz} \mathrm{AC}$source is:

When an electrical device $X$ is connected to $a220 \mathrm{V},50 \mathrm{Hz}$ ac supply, the current is $0.5 \mathrm{A}$ and is in same phase as the applied voltage. When another device $Y$ is connected to the same supply, the electric current is again $0.5 \mathrm{A}$ but it leads the potential difference by $\frac{\pi }{2}.$

What are the devices $X$ and $Y$?

An $AC$ voltage $V=V_0\sin 100 t$ is applied to the circuit, the phase difference between current and voltage is found to be $\frac{\mathrm{\pi }}{4},$ then

A sinusoidal voltage of peak value 283 V and frequency 50 Hz is applied to a series LCR circuit in which $R=3 \Omega$, $L=25.48 mH$ and $C=796 \mu F.$ The impedance of the circuit.

A capacitor and a resistor are connected in series with an ac source. If the potential difference across $C$ and $R$ are $120 \mathrm{V}$ and $90 \mathrm{V}$ respectively and if the rms current of the circuit is $3 \mathrm{A},$ calculate the

impedence,

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$

When an electrical device $X$ is connected to $a220 \mathrm{V},50 \mathrm{Hz}$ ac supply, the current is $0.5 \mathrm{A}$ and is in same phase as the applied voltage. When another device $Y$ is connected to the same supply, the electric current is again $0.5 \mathrm{A}$ but it leads the potential difference by $\frac{\pi }{2}.$

When $X$ and $Y$ are connected in series across the same source, what will be the current?

A bulb B and a capacitor $C$ are connected in series to the ac mains as shown in Fig. The bulb glows with some brightness. How will the glow of the bulb change when a dielectric slab is introduced between the plates of the capacitor ? Give reasons in support of your answer ?

A time $\mathrm{t}=0$0$, a battery of $10 \mathrm{V}$ is connected across points $\mathrm{A}$ and $\mathrm{B}$ in the given circuit, Fig If the capacitors have no charge initially, at what time (in second) does the voltage across them becomes $4 \mathrm{V}$.

A capacitor and a resistor are connected in series with an ac source. If the potential difference across $C$ and $R$ are $120 \mathrm{V}$ and $90 \mathrm{V}$ respectively and if the rms current of the circuit is $3 \mathrm{A},$ calculate the

power factor of the circuit.

When an alternating voltage of $220 \mathrm{V}$ is applied across a device $P$, a current of $0.25 \mathrm{A}$ Flows through the circuit, and it leads the applied voltage by an angle $\frac{\mathrm{\pi }}{2} \mathrm{radian}$ . When the same voltage source is connected across another device $Q$, the same current is observed in the circuit but in phase with the applied voltage. What is the current when the same source is connected across a series combination of $P$ and $Q$.

When an $\mathrm{AC}$ source of emf $\mathrm{e}={\mathrm{E}}_0\sin 100\mathrm{t}$ is connected across a circuit, the phase-difference between the emf $\mathrm{e}$ and
the current $\mathrm{i}$ in the circuit is observed to be $\frac{\mathrm{\pi }}{4}$, as shown in Fig. If the circuit consists possibly only of $\mathrm{R}-\mathrm{C}$ or $\mathrm{R}$ $\mathrm{L}$ or $\mathrm{L}-\mathrm{C}$ in series, find the relationships between the two elements.