$A$ $220 \; V, 50 \; Hz$ $AC$ source is connected to a $25 \; V, 5 \; W$ lamp and an additional resistance $R$ in series (as shown in the figure) to run the lamp at its rated power. The value of $R$ (in $\Omega$) will be:

Consider the $L-C-R$ circuit given below. The circuit is driven by a $50 \,Hz, AC$ source with peak voltage $220 \,V$. If $R=400 \,\Omega, C=200 \,\mu F$ and $L=6 \,H$,the maximum current in the circuit is closest to ............ $A$.

As given in the figure,a series circuit connected across a $200\, V$,$60\, Hz$ line consists of a capacitor of capacitive reactance $30\,\Omega$,a non-inductive resistor of $44\,\Omega$,and a coil of inductive reactance $90\,\Omega$ and resistance $36\,\Omega$. The power dissipated in the coil is......$W$

$A$ series $LCR$ circuit containing a resistance of $120 \, \Omega$ has an angular resonance frequency of $4 \times 10^3 \, rad \, s^{-1}.$ At resonance, the voltages across the resistance and the inductance are $60 \, V$ and $40 \, V$ respectively. The values of $L$ and $C$ are respectively:

$A$ series $LCR$ circuit has $R=200 \Omega$, $L=663 \text{ mH}$, and $C=26.5 \mu F$. The applied alternating voltage has an amplitude of $50 \text{ V}$ and a frequency of $60 \text{ Hz}$ such that $X_{L}=250 \Omega$ and $X_{C}=100 \Omega$. The peak current is: (in $\text{ A}$)

In the given circuit,the peak voltages across $C$,$L$,and $R$ are $30 \,V$,$110 \,V$,and $60 \,V$,respectively. The rms value of the applied voltage is (in $\,V$)