Correct Answer: a

Explanation: 3 _A_ ​$\eta = \frac{\&\text{nbsp};\text{Output}\&\text{nbsp};}{\&\text{nbsp};\text{Input}\&\text{nbsp};}$​​ ​$\Rightarrow \frac{80}{100} = \frac{20 \times 120}{1000 \times i_{1}}$​​ ​$\Rightarrow i_{1} = \frac{20 \times 120 \times 100}{1000 \times 80} = 3 \&\text{nbsp}; A$​​ ​$\Rightarrow i_{1} = 3 \&\text{nbsp}; A$​​

Correct Answer: c

Explanation: ${\displaystyle \frac{1}{\sqrt2}{\left({i}_{1}^{2}+{i}_{2}^{2}\right)}^{1/2}}$   $\begin{matrix}i_{r m s} = \sqrt{\left(\frac{i_{1}}{\sqrt{2}}\right)^{2} + \left(\frac{i_{2}}{\sqrt{2}}\right)^{2}} \\ = \frac{1}{\sqrt{2}} = \left(i_{1}^{2} + i_{2}^{2}\right)^{1 / 2}\end{matrix}$

Correct Answer: c

Explanation: 50.3% $\begin{matrix}\frac{R}{Z_{1}} = cos = 0.75 a n d \frac{R}{Z_{2}} = cos _{2} = 0.5 \\ Z_{1} = \frac{R}{0.75} = 1.33 R a n d Z_{2} = 2 R \\ Z = Z_{2} Z_{1} = \left(2 1.33\right) R = 0.67 R \\ i n c r e a s e i n i m p e d a n c e = \frac{ Z}{Z} 100 \\ = \frac{0.67 R}{1.33 R} 100 = 50.3 \end{matrix}$

Correct Answer: c

Explanation: ​$\frac{E_0^2}{4 R}$​​

Correct Answer: c

Explanation: power factor of circuit will be unity if capacitive reactance equals inductive reactance $\begin{matrix}T h e c i r c u i t w i l l h a v e i n d u c t i v e n a t u r e i f > \frac{1}{\sqrt{L C}} \left( t > \frac{1}{\sqrt{L C}}\right) \\ H e n c e , \left(a\right) i s f a l s e . A l s o i f c i r c u i t h a s i n d u c t i v e n a t u r e t h e c u r r e n t w i l l \\ log b e h i n d v o l t a g e . H e n c e \left(d\right) i s a l s o f a l s e . \\ i f = \frac{1}{\sqrt{L C}} \left( l = \frac{1}{\sqrt{L C}}\right) t h e c i r c u i t w i l l h a v e r e s i s tive in n a t u r e . \\ H e n c e B i s f a l s e P o w e r f a c t o r cos = \frac{R}{\sqrt{R^{2} + \left( L + \frac{1}{ C}\right)}} = 1 \\ i t L = \frac{1}{ C} . H e n c e C i s t r u e .\end{matrix}$