Electric Circuit Analysis: Chapter - 3: Basic Circuit Analysis - AC
Effective (RMS) Value
AC Circuit Analysis
he heat produced by an alternating current of maximum value say Im will not be equal to the heat produced by a direct current of Im amperes.
EFFECTIVE (RMS) VALUE
When
a current passes through a resistor, heat is produced irrespective of the
direction of current flow. The heat produced by an alternating current of
maximum value say Im will not be equal to the heat produced by a
direct current of Im amperes. The effective value of an alternating
current is the value of steady direct current which produces the same heat as
that produced by the alternating current when passed through the same resistor
for the same interval of time.
If
i (t) is the time varying current passed through a resistor of R ohms, then for
a small interval of time, dt seconds, the heat produced, dH is equal to
dH
= i2 (t) R dt
Over
one complete cycle,
If
this heat is equal to the heat produced by a steady DC of I amperes passed
through R for T seconds, then
This
definition explains why the effective value is also called the root mean square
(RMS) value. The RMS value of a wave may also be determined by finding the area
under the squared curve as below.
Where
i1,i2,i3,… iN are instantaneous
values.
Electric Circuit Analysis: Chapter - 3: Basic Circuit Analysis - AC : Tag: : AC Circuit Analysis - Effective (RMS) Value