The circuit shown in the figure has two sources connected in series. The instantaneous voltage of the AC source (in volt) is given by v(t) = 12sint. If the circuit is in steady-state, then the rms value of the current (in Ampere) flowing in the circuit is ______.

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