AC Circuits Questions

What is the value of inductance $L$ for which the current is a maximum in a series $LCR$ circuit with $C=10\mu \text{F}$ and $\omega =1000{\text{s}}^{-1}$?

The primary and secondary coils of a transformer have $50$ and $1500$ turns respectively. If the magnetic flux $\varphi$ linked with the primary coil is given by $\varphi ={\varphi }_0+4t$, where $\varphi$ is in weber, $t$ is time in second and ${\varphi }_0$ is a constant, the output voltage across the secondary coil is:

A transformer is used to light a $100\text{W}$ and $110\text{V}$ lamp from a $220\text{V}$ mains. If the main current is $0.5\text{A}$, the efficiency of the transformer is approximately:

A small signal voltage $V(t)=V_0\sin \omega t$ is applied across an ideal capacitor $C$:

An inductor $20\text{mH}$, a capacitor $50\mu \text{F}$ and a resistor $40\Omega$ are connected in series across a source of emf $V=10\sin 340t$. The power loss in A.C. circuit is: