For the given variant of alternating Current circuit (Table 2): 1) To deter mine the current in the citcuit and voltage across each of the elements. 2) To built current and vobbage voetor diagram. 3)Ta determine the ralue of the regctance at which voltage resonance, arise and the value of resonance crrend through the circuit.

We are authorized to answer one question at a time, since you have not mentioned which question you are looking for, so we are answering the first one(problem no.3). Please repost your question separately for the remaining question.

Here supply voltage frequency is not given so we will assume supply frequency as 'f' and obtain the answers in terms of s

' f '

Problem 3:

From the second option of the table

$$\begin{gathered} R_1=6 \Omega \\ {R}_2=2 \Omega \\ {L}_1=20 mH \\ {L}_2=15 mH \\ {C}_1=260 \mu F \\ {C}_2 =1600 \mu F \end{gathered}$$

V=6 V

1) Given circuit is  RLC series circuit and hence current will be remain same in all the elements.

$$\begin{gathered} {X}_L=wL =2\pi fL =2\pi f(L_1+L_2) \\ {X}_L =2\pi f(20\times {10}^{-3}+ 15\times {10}^{-3}) \\ {X}_L =0.22 f \\ {X}_c=\frac{1}{2\pi fC} =\frac{1}{2\pi f(C_1+C_2)} \\ {X}_c =\frac{1}{2\pi f(260 \mu F+1600 \mu F)} \\ {X}_c =\frac{85.57}{f} \end{gathered}$$

1)Current in the circuit

                                                 $$\begin{gathered} I =\frac{V}{Z} =\frac{6}{R +j(X_L-X_c)} \\ R=R_1+R_2 =6+2 =8 \Omega \\ I=\frac{6}{8 +j(0.22f-{\displaystyle \raisebox{1ex}{$85.57$}\!\left/ \!\raisebox{-1ex}{$f$}\right.})} \end{gathered}$$

voltage across each element

    $$\begin{gathered} V_{L1}=I{X}_{L1} =I\left(2\pi f{L}_1\right) = I(2\pi f\times 20\times {10}^{-3}) \\ =\frac{6}{8 +j(0.22f-{\displaystyle \raisebox{1ex}{$85.57$}\!\left/ \!\raisebox{-1ex}{$f$}\right.})} \times (0.1256f) \\ {\mathit{V}}_{\mathbf{L}\mathbf{1}} =\frac{0.75f}{8 +j(0.22f-\raisebox{1ex}{$85.57$}\!\left/ \!\raisebox{-1ex}{$f$}\right.)} \\ {V}_{L2}=I{X}_{L2} =I\left(2\pi f{L}_2\right) = I(2\pi f\times 15\times {10}^{-3}) \\ =\frac{6}{8 +j(0.22f-{\displaystyle \raisebox{1ex}{$85.57$}\!\left/ \!\raisebox{-1ex}{$f$}\right.})} \times (0.0942f) \\ {\mathit{V}}_{\mathbf{L}\mathbf{2}} =\frac{0.565 f}{8 +j(0.22f-\raisebox{1ex}{$85.57$}\!\left/ \!\raisebox{-1ex}{$f$}\right.)} \end{gathered}$$