
Electric Generator The armature in an electric generator is rotating at the rate of 100 revolutions per second (rps). If the maximum voltage produced is 310 V, find an equation that describes this variation in voltage. What is the RMS voltage? (See Example 6 and the margin note adjacent to it.)

The equation that describes the variation of voltage and the RMS voltage.
Answer to Problem 42E
The equation that describes the variation of voltage is E(t)=310cos200πt and the root mean square voltage is 219 V.
Explanation of Solution
Given:
The armature is rotating at the rate of 100 revolutions per second. The maximum voltage produced is 310 V.
Formula used:
Voltage generated at time t is given by,
E(t)=E0cosωt (1)
Where,
E0 is the maximum voltage, ω2π is the number of revolutions per second.
Calculation:
Formula to calculate ω is,
Revolutions per second=ω2π
Substitute 100 for revoluations in the above formula.
100=ω2πω=100×2πω=200π
The maximum voltage is 310 V.
Substitute 310 for E0 and 200π for ω, in equation (1).
E(t)=310cos200πt
The root mean square voltage is 1√2 times the maximum voltage.
RMS voltage=Maximum voltage√2
Substitute 310 V for maximum voltage in the above formula.
RMS voltage=310√2=3101.414≈219 V
Therefore, the equation that describes the variation of voltage is E(t)=310cos200πt and the root mean square voltage is 219 V.
Chapter 5 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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