In a radio receiver,the short wave and medium wave stations are tuned by using the same capacitor but coils of different inductance $L_s$ and $L_m$ respectively. Then:

The value of the alternating emf in the given series $LCR$ circuit is: (in $V$)

Consider the parallel $LCR$ circuit shown in the figure. Find the net current $i$ and the phase of $i$. Show that $i = \frac{V}{Z}$. Find the impedance $Z$ for this circuit.

The average power consumed by the given circuit is $W$.

In the circuit shown in the figure,if both the bulbs $B_1$ and $B_2$ are identical,then:

An inductor of $10 \text{ mH}$, capacitor of $0.1 \text{ } \mu\text{F}$ and a resistor of $100 \text{ } \Omega$ are connected in series across an $a.c.$ power supply of $220 \text{ V}$, $70 \text{ Hz}$. The power factor of the given circuit is $0.5$. The difference between the inductive reactance and capacitive reactance is $\sqrt{3}\alpha \text{ } \Omega$. The value of $\alpha$ is . . . . . . .