Question

A capacitor and resistor are connected with an $AC$ source as shown in figure. Reactance of capacitor is $X_C=3\Omega$ and resistance of resistor is $4\Omega$. Phase difference between current $I$ and $I_1$ is $[{\tan }^{-1}\left(\frac{3}{4}\right)={37}^o]$

• A. ${90}^o$
• B. zero
• C. ${53}^o$
• D. ${37}^o$

Answer 1

Answer: (C)

${53}^o$

$I_2=\frac{V}{X_C}=\frac{V}{3}$ $(V=rms$ value)
$I_1=\frac{V}{R}=\frac{V}{4}$
$I_2$ is ${90}^o$ ahead of applied voltage function and $I_1$ is in phase with it.
$\tan \varphi =\frac{V/3}{V/4}=\frac{4}{3}$
$\therefore \varphi ={53}^o$.