A series RLC circuit is observed at two frequencies. At $$\omega_1$$ = 1k rad / s, we note that source voltage $$V_1=100\angle0^\circ V$$ results in a current $$I_1=0.03\angle31^\circ\;A$$. At $$\omega_2$$ = 2 k rad/s, the source voltage $$V_2=100\angle0^\circ\;V$$ results in a current $$I_2=2\angle0^\circ\;A$$. The closest values for R,L,C out of the following options are

The total power dissipated in the circuit, show in the figure, is 1kW. The ideal voltmeter, across the load, reads 200 V. The value of X_L is _________.

The voltage across the capacitor, as sown in the figure, is expressed as $$$V_c\left(t\right)=A_1\sin\left(\omega_1t-\theta_1\right)+A_2\sin\left(\omega_2t-\theta_2\right)$$$ The value of A₁ and A₂ respectively, are

Two magnetically uncoupled inductive coils have Q factors q₁ and q₂ at the chosen operating frequency. Their respective resistances are R₁ and R₂ . When connected in series, their effective Q factor at the same operating frequency is