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Electricity and Basic Electronics
Math Focus 12-1: Square Roots
In upcoming chapters and in the following section, you will
need to calculate the square root of numbers. A square root is related
to the base of a number that is squared, or that has an exponent of 2,
such as 42. You should recall from Chapter 3 that an exponent is a
number that tells how many times to multiply another number by
itself. When a number is squared, it is only multiplied by itself one
time. Therefore,
42 = 4 × 4
You know that 42 is equal to 16. The square root of 16 then is a
number that when multiplied by itself gives that value.
42 = 4 × 4 = 16
A formula that says you need to fi nd the square root of 16 is
written as follows:
√16
___
Invert both sides of the equation:
L
T
=
12
_______
13 mH
= 0.923 mH
This circuit has a total inductance of 0.923
mH, or 923 μH.
Example 12-2:
Suppose a parallel circuit has two branches,
and each branch contains an inductor. The
Figure 12-13. Three inductors are wired in
parallel with the ac power supply.
L1 = 2 mH L3 = 4 mH L2 = 3 mH
fi rst inductor (L
1
) has an inductance of
130 μH, and the second inductor (L
2
) has
an inductance of 260 μH. What is the total
inductance (L
T
) for this circuit?
1
__
L
T
=
1
__
L
1
+
1
__
L
2
=
1
_______
130 μH
+
1
_______
260 μH
=
2
_______
260 μH
+
1
_______
260 μH
=
3
_______
260 μH
Invert both sides of the equation:
L
T
=
260
_____
3 μH
= 86.7 μH
The total inductance for this circuit is 86.7 μH.
The same concept used to solve total
resistance in series-parallel circuits can be
used to analyze inductor values. Consider