Chapter 32, Problem 1CQ

To determine

a) Instantaneous value of emf

b) If the magnitude of each emf increasing, decreasing or holding constant.

Answer to Problem 1CQ

Solution:

For phasor a.

a) Instantaneous emf = $-100\text{ V}$

b) emf is decreasing.

For phasor b.

a) Instantaneous emf = $60\text{ V}$

b) emf is decreasing.

For phasor c.

a) Instantaneous emf = $80\text{ V}$

b) emf is increasing.

Explanation of Solution

Given:

The following figure showing phasors are given.

Explanation:

From the figure we can find the value of the emf of each of the phasors.

For phasor a

a) The instantaneous value of emf = $-100\text{ V}$

b) The phasor rotates counter clockwise, as phasor a rotates it comes near to the vertical axis and goes away from the horizontal axis, hence the magnitude of emf is decreasing.

For phasor b

a) The instantaneous value of emf = $60\text{ V}$

b) The phasor rotates counter clockwise, as phasor b rotates it comes near to the vertical axis and goes away from the horizontal axis, hence the magnitude of emf is decreasing.

For phasor c

a) The instantaneous value of emf = $80\text{ V}$

b) The phasor rotates counter clockwise, as phasor c rotates it comes near to the horizontal axis and goes away from the vertical axis, hence the magnitude of emf is increasing.

Conclusion:

For phasor a: The instantaneous emf is $-100\text{ V}$, and the magnitude is decreasing.

For phasor b: The instantaneous emf is $60\text{ V}$, and the magnitude is decreasing.

For phasor c: The instantaneous emf is $80\text{ V}$, and the magnitude is increasing.