The phase difference between the alternating current and emf is $\frac{\pi}{2}$. Which of the following cannot be the constituent of the circuit?

An $AC$ circuit has an inductor and a resistor of resistance $R$ in series,such that $X_L = 3R$. Now,a capacitor is added in series such that $X_C = 2R$. The ratio of the new power factor to the old power factor of the circuit is $\sqrt{5} : x$. The value of $x$ 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

$A$ light bulb and an open coil inductor are connected to an $AC$ source through a key as shown in the figure. The switch is closed and after some time,an iron rod is inserted into the interior of the inductor. Does the glow of the light bulb $(a)$ increase,$(b)$ decrease,or $(c)$ remain unchanged? Give your answer with reasons.

In an $AC$ circuit,a resistance of $R \, \Omega$ is connected in series with an inductance $L$. If the phase angle between voltage and current is $45^o$,the value of inductive reactance will be:

In a series $LCR$ circuit, the potential drop across $L, C$ and $R$ respectively are $40 \,V, 120 \,V$ and $60 \,V$. Then the source voltage is (in $\,V$)