Question

Draw the phasor for the emf $\epsilon =\left(170\right)\cos \left(\right(2\pi \times 60hz\left)t\right)$at$t=60ms$

Short answer

Required figure is given below.

Step-by-step solution

Given information

We need to draw phasor diagram of given equation$\epsilon =\left(170\right)\cos \left((2\pi \times 60Hz\right)t)att=60ms$

Explanation

We are given an expression for the instantaneous emf by

$\in =\left(170V\right)\cos \left(\left(2\pi \times 60Hz\right)t\right)$

We know that the general expression of instantaneous emf

$\in ={\in }_{\circ }\cos \left(wt+\varphi \right)$

By comparing both equation

$$\begin{gathered} \theta =\left(2\pi \times 60Hz\right)t \\ \theta =\left(2\pi \times 60Hz\right)\left(60\times {10}^{-3}s\right) \\ \theta =22.62rad \\ \theta ={216}^{\circ } \end{gathered}$$

Now, we can draw the phasor by rotating counterclockwise ${216}^{\circ }$from positive x-axis till the instantaneous emf becomes $-137.5V$as shown below.