A 12 V resistance and an inductance of \(\frac { 0.05 }{ \pi } H\)  are connected in series.Across the end of this ciuit an alternating voltage of 130 V and frequency 50 Hz is connected. Calculate the current in the circuit and the potential difference across the inductance.

In a series L-C-R circuit connected to an AC source of variable frequency and voltage \(V\ =\ { V }_{ m }\ sin\ \omega t\), draw a plot showing the variation of current I with angular frequency \(\omega \), for two different values of resistance R₁and R₂(R₁>R₂). Write the condition under which the phenomenon of resistance occurs. For which value of the resistance out of the two curves, a sharper resonance is produced? Define Q-factor of the circuit and give its significance.

An AC voltage \(V={ V }_{ m }sin \ \omega t\) is applied across an inducer of inductance L.Find the instantaneous power P_i supplied to the inductor. Show graphically the variation of P_i with \(\omega t\) .

(i) Determine the value of phase difference between the current and the voltage in the given series L-C-R circuit.

(ii) Calculate the Value of additional capacitor which may be joined suitably to the capacitor C that would make the power factor of the circuit unity.

Study the circuits (a) and (b) shown in the figure answer the following question:

(i) Under which conditions would the rms currents in the two circuits be the same?
(ii) Can the rms current in circuit (b) be larger than that in (a)?