An alternating voltage is applied to a series $LCR$ circuit. If the current leads the voltage by $45^{\circ}$,then $\left(\tan 45^{\circ}=1\right)$:

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 $W$)

When an $AC$ source of emf $E$ with angular frequency $\omega = 100 \text{ rad/s}$ is connected across a circuit,the phase difference between $E$ and current $I$ in the circuit is observed to be $\frac{\pi}{4}$ as shown in the figure. If the circuit consists of only $RC$ or $RL$ in series,then:

An a.c. source of frequency $f$ is connected to a circuit containing an inductance $L$ and resistance $R$ in series. The impedance of this circuit is

An alternating current of frequency $f$ is flowing in a circuit containing a resistance $R$ and a choke $L$ in series. The impedance of this circuit is

An ideal choke draws a current of $8 \, A$ when connected to an $AC$ supply of $100 \, V, 50 \, Hz$. $A$ pure resistor draws a current of $10 \, A$ when connected to the same source. The ideal choke and the resistor are connected in series and then connected to the $AC$ source of $150 \, V, 40 \, Hz$. The current in the circuit becomes