Exercise-2

Power factor of an $L-R$ series circuit is $0.6$ and that of a $C-R$ series circuit is $0.5$. If element ($L,C$ and $R$ of the two circuit are joined in series the power factor of this circuit is found to be $1$. The ratio of the resistance in the $L-R$ circuit to the resistance in the $C-R$ circuit is

The effective value of current $i=2\sin 100\pi t+2\sin \left(100\pi t+30°\right)$ is

If $I_1, I_2, I_3$ and $I_4$ are the respective r.m.s. values of the time varying currents as shown in the four cases $\mathrm{I}, \mathrm{II}, \mathrm{III}$ and $\mathrm{IV}$. Then identify the correct relations

An a.c. source of voltage $V$ and of frequency $50 \mathrm{Hz}$ is connected to an inductor of $2 \mathrm{H}$ and negligible resistance. A current of r.m.s. value $I$ flows in the coil. When the frequency of the voltage is changed to $400 \mathrm{Hz}$ keeping the magnitude of $V$ the same, the current is now

Let $f=50 \mathrm{Hz},$ and $C=100 \mathrm{\mu F}$ in $\mathrm{AC}$ circuit containing a capacitor only. If the peak value of the current in the circuit is $1.57 \mathrm{A}$ at $t=0.$ The expression for the instantaneous voltage across the capacitor will be

In the circuit diagram shown, $X_C=100 \mathrm{\Omega }, {\mathrm{X}}_{\mathrm{L}}=200\mathrm{\Omega }$ and $R=100 \mathrm{\Omega }.$ The effective current through the source is

In the shown $\mathrm{AC}$ circuit phase different between currents $I_1$ and $I_2$ is

For a $\mathrm{LCR}$ series circuit with an $\mathrm{A}.\mathrm{C}.$ source of angular frequency $\omega :$