The initial phase angle for $\mathrm{i}=10\mathrm{sin\omega t}+8\mathrm{cos\omega t}$ is

When an $\mathrm{AC}$ source of emf $\mathrm{e}={\mathrm{E}}_0\sin 100\mathrm{t}$ is connected across a circuit, the phase-difference between the emf $\mathrm{e}$ and
the current $\mathrm{i}$ in the circuit is observed to be $\frac{\mathrm{\pi }}{4}$, as shown in Fig. If the circuit consists possibly only of $\mathrm{R}-\mathrm{C}$ or $\mathrm{R}$ $\mathrm{L}$ or $\mathrm{L}-\mathrm{C}$ in series, find the relationships between the two elements.

The power loss in Ac circuit will be minimum when

A circuit draws $220 \mathrm{W}$ from a $110 \mathrm{V},60 \mathrm{Hz}$ AC line. The power factor is $0.6$ and the current lags the voltage. The capacitance of a series capacitor that will result in a power factor of unity is equal to

For the series $\mathrm{L}-\mathrm{C}-\mathrm{R}$ circuit shown in the Fig. What is the resonance frequency and the amplitude of the current at the resonating frequency