MATHEMATICAL
CALCUUTIONS
AND DEFINITIONS
Purpose: To demonstrate that the previous experience is
in agreement with the mathematical formulas
The following formulas are used to calculate ROOT MEAN
SQUARE, PEAK and PEAK-to-PEAK AC sine wave Volt-
ages, Refer to Fig. 32.
V
P
=
1.414 x
vrms
V
p=.
5
x
vp_p
V
P-P
=
2.828 x
Vrms
V
P-P
=
2xvp
V
fms
=
.707
x vp
V
fms
=
.3536
x
Vp_p
PEAK VALUE (p): The amplitude of a voltage measured
from zero or reference axis to its maximum value, when the
voltage alternates between positive and negative half
cycles.
PEAK-to-PEAK (p-p): The amplitude of a voltage meas-
ured from maximum positive peak to maximum negative
peak, when the voltage alternates between positive and
negative half cycles.
ROOT MEAN SQUARE (RMS): The effective or RMS val-
ue of a voltage is the SQUARE ROOT of the average
(MEAN) of the squares of all the instantaneous values of
the voltage over one cycle. For a sine voltage, the
RMS
vai-
ue is equal to 0.707 times the maximum peak value of the
voltage.
INSTANTANEOUS VALUE: The exact value of the ampli-
tude of a voltage at a particular instant in time.
Using the above formulas, calculate the unknown voltages
in Fig. 35.
This completes the AC VOLTAGE OBSERVATION and
MEASUREMENT EXPERIENCE.
Have your instructor
initial your progress guide.
MEASURED
VALUE
RMS
PEAK-TO-PEAK
PEAK
54Vp-p
115vlms
163vp
,
326vp-p
.
FIG.
35
71
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