$A$ resistor of $500 \Omega$ and an inductor of $0.5 \ H$ are connected in series with an $AC$ source given by $V = 100 \sqrt{2} \sin(1000 t)$. The power factor of the combination is:

$A$ sinusoidal voltage $V(t) = 210 \sin(3000t) \text{ V}$ is applied to a series $LCR$ circuit in which $L = 10 \text{ mH}$,$C = 25 \mu\text{F}$,and $R = 100 \Omega$. The phase difference $(\Phi)$ between the applied voltage and resultant current will be

An $AC$ generator $10 \, V$ (rms) at $200 \, rad/s$ is connected in series with a $50 \, \Omega$ resistor, a $400 \, mH$ inductor, and a $200 \, \mu F$ capacitor. The rms voltage across the inductor is (in $V$)

In an $LR$ circuit,the value of $L$ is $(\frac{0.3}{\pi}) \ H$ and the value of $R$ is $40 \ \Omega$. If an alternating e.m.f. of $230 \ V$ at $50 \ Hz$ is connected to the circuit,what are the impedance and the current in the circuit,respectively?

$A$ coil of resistance $450 \Omega$ and self-inductance $1.5 \text{ H}$ is connected to an $A$.$C$. source of frequency $\frac{150}{\pi} \text{ Hz}$. The phase difference between voltage and current is

In an $LC$ circuit,the inductance $L = 40 \; mH$ and capacitance $C = 100 \; \mu F$. If a voltage $V(t) = 10 \sin (314 t)$ is applied to the circuit,the current in the circuit is given by: