$A$ 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

In the given circuit,the angular frequency of the voltage source is $70 \times 10^3 \text{ rad s}^{-1}$. The circuit effectively behaves like,

An $ac$ source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current registered is $I$. If the frequency of the source is changed to $\omega/3$ (while maintaining the same voltage),the current in the circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency $\omega$.

In the given figure,the current amplitude is

In a series $L-C-R$ circuit,

An alternating emf given by the equation $E = 200 \sin(50 \pi t)$ (where $E$ is in volts and $t$ is in seconds) is applied across a series combination of an inductor and a resistor having inductive reactance $X_L = 40 \ \Omega$ and resistance $R = 30 \ \Omega$ respectively. At time $t = 1 \ s$,the power dissipated by the resistor is close to $(\cos 53^{\circ} = 0.6)$. (in $W$)