In a circuit consisting of a capacitance and a generator with alternating emf, $E_g=E_{go}sin\omega t, V_C$ and $I_{\mathit{C}}$ are the voltage and current. Correct phasor diagram for such circuit is

Two circuits are shown in figure $\left(a\right)$ and $\left(b\right)$. At a frequency of _______ $\mathrm{rad} {\mathrm{s}}^{-1}$ the average power dissipated in one cycle will be the same in both the circuits.

Consider an electrical circuit containing a two way switch $S.$ Initially $S$ is open and then $T_1$ is connected to $T_2.$ As the current in $R=6 \mathrm{\Omega }$ attains a maximum value of steady-state level, $T_1$ is disconnected from $T_2$ and immediately connected to $T_3.$ Potential drop across $r=3 \mathrm{\Omega }$ resistor immediately after $T_1$ is connected to $T_3$ is $\_\_\_\_\_\_\mathrm{V}.$ (Round off to the Nearest Integer)

In the given figure the magnetic flux through the loop increases according to the relation ${\varphi }_B\left(t\right)=10t^2+20t$, where ${\varphi }_B$ is in milliwebers and $t$ is in seconds. The magnitude of current through $R=2 \mathrm{\Omega }$ resistor at $t=5 \mathrm{s}$ is _____ $\mathrm{mA}.$

A conducting bar of length $L$ is free to slide on two parallel conducting rails as shown in the figure.

Two resistors $R_1$ and $R_2$ are connected across the ends of the rails. There is a uniform magnetic field $\overrightarrow{B}$ pointing into the page. An external agent pulls the bar to the left at a constant speed $v$.

The correct statement about the directions of induced currents $I_1$ and $I_2$ flowing through $R_1$ and $R_2$ respectively is :

For the given circuit, comment on the type of transformer used :