Question

The instantaneous value of current at a given instant is$1A$ and peak value of current is $\frac{5}{3}A$. The potential difference between $P$ and $Q$ at the same instant is

• A. $\frac{23}{3}V$
• B. $7V$
• C. $3V$
• D. $4V$

Answer 1

The correct option is A $\frac{23}{3}V$

$\begin{array}{c}Leti=i_{\circ }\sin wt\\ \Rightarrow i=\frac{5}{3}\sin wt\\ \Rightarrow \sin wt=\frac{3}{5}.......\left(1\right)\\ \Rightarrow V=V_{\circ }\sin \left(wt+\varphi \right)\\ \Rightarrow V_{\circ }=\frac{5}{3}\left(5\right)=\frac{25}{3}\\ \Rightarrow \tan \varphi =\frac{4}{3}\\ \Rightarrow \theta ={53}^{\circ }\\ \Rightarrow V=\frac{25}{3}\left[\sin wt+{53}^{\circ }\right]\\ =\frac{25}{3}\left[\sin wt\cos {53}^{\circ }+\cos wt\sin {53}^{\circ }\right]\\ \Rightarrow V=\frac{23}{3}V\\ Hence,\\ optionAiscorrectanswer.\end{array}$