Sample Solution from
Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN: 9781305632134
Chapter 2
Problem 2.1MCQ
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Textbook Problem

The rms value of v ( t ) = V max cos ( ω t + δ ) is given by

a. V max

b. V max / 2

c. 2V max

d. 2 V max

Expert Solution
To determine

The rms value of the voltage function v(t).

Answer

The option (b) is correct, therms value of the voltage function v(t) is Vmax2.

Explanation of Solution

Given:

The expression for voltage v(t) is.

v(t)=Vmaxcos(ωt+δ)

Concept used:

Write the standard sinusoidal expression for voltage v(t).

v(t)=vmcos(ωt+ϕ)   ...............(1)

Here, vm is the maximum value of sinusoidal voltage, ω is angular frequency, t is the time and ϕ is the phase shift.

Write the expression for rms value of voltage.

vrms=vm2   ...............(2)

Here, vrms is the rms value of voltage.

Calculation:

Compare equation (1) with given expression.

vm=Vmax

Substitute Vmax for vm in equation (2).

vrms=Vmax2

The rms value of the voltage function v(t) is Vmax2.

Conclusion:

Thus, option (b) is correct, therms value of the voltage function v(t) is Vmax2.

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