The circuit shown in the figure is energized by a sinusoidal voltage source $${V_1}$$ at a frequency which causes resonance with a current of $${\rm I}$$.

The phasor diagram which is applicable to this circuit is

The $$RL$$ circuit of the figure is fed from a constant magnitude, variable frequency sinusoidal voltage source $${V_{IN.}}$$ At $$100Hz,$$ the $$R$$ and $$L$$ elements each have a voltage drop $${u_{RMS}}.$$ If the frequency of the source is changed to $$50Hz,$$ then new voltage drop across $$R$$ is

In Fig. the admittance values of the elements in Siemens are
$${Y_R} = 0.5 + j0,$$
$${Y_L} = 0 - j\,1.5,$$
$${Y_C} = 0 + j\,0.3$$ respectively.
The value of $${\rm I}$$ as a phasor when the voltage $$E$$ across the elements is $$10\angle {0^0}\,V$$ is

In the circuit of Fig. the magnitudes of $${V_L}$$ and $${V_C}$$ are twice that of $${V_R}$$. The inductance of the coil is