17.1 Useful Formulas
Effect of temperature on resistance: Coil resistance specifications are given
for an ambient temperature of 25° C. The resistance of copper varies
linearly with temperature. This variation can be stated as:
where
R1 = initial resistance
R2 = resistance at new temperature
T1 = initial temperature or ambient
T2 = new ambient temperature
To convert a known coil resistance at 25° C to a resistance at a different
temperature, multiply by the temperature correction factor obtained from the
above formula.
Maximum wattage for relay coils: When electrical current is passed through a
coil, the temperature of the coil will rise until the rate of heat dissipation
is equal to the rate of heat generation. The deterioration of the insulation of
the windings due to the temperature attainted is generally the current limiting
factor. A "self-protecting" coil is one in which the maximum temperature
reached (with normal confinement and maximum expected ambient temperature) when
the specified current is passed continuously through the coil is below the
point causing injury to the coil insulation at its hottest spot. The mean
temperature of a coil winding in ° C can be calculated as follows:
where
Rc = resistance at cold, or pre-energized,
temperature
Rt = measured resistance at the elevated
temperature
Tc = temperature of the coil prior to energization
in ° C
Impedance: In any ac circuit where resistance and reactance values of the R,
L, and C components are given, the absolute or numerical magnitude
of impedance and phase angle can be computed from the formulas which
follow.
The basic formulas expressing total impedance for series circuits are:
and for parallel circuits:
In series circuits where phase angle and any two of the Z, R and
X components are known, the unknown component may be determined from the
following expressions:
where Z = magnitude of impedance in ohms, R = resistance in
ohms, and X = reactance (inductive or capacitive) in ohms.
Typical numerical values of impedance:
Nomenclature: Z = absolute or numerical value of impedance value in
ohms
R = resistance in ohms
XL = inductive reactance in ohms
Xc = capacitive reactance in ohms
L = inductance in henrys,
C = capacitance in farads
RL = resistance in ohms acting in series with
inductance
RC = resistance in ohms acting in series with
capacitance
Ø = phase angle in degrees by which current leads
voltage in a capacitive circuit or lags voltage in an inductive circuit. In a
resonant circuit, where XL = XC, Ø = 0.
resistance, inductance, and capacitance in series
inductance, resistance, and capacitance in parallel
capacitance and series resistance in parallel with inductance and series
resistance
To find terminal velocity required for a particular shock pulse, draw line connecting peak acceleration
with pulse duration. Example: 60g, 10ms: line 1 -1.
Draw horizontal line from intersection. point (3). of of line (1) - (2) and reference
line to velocity of pulse shape that is required. Velocity required to product 60g, 10ms
saw-tooth pulse 120 in/s point (4).
