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I'm reading on air "gap impedance" and came across this equation from these notes on the topic. http://web.mit.edu/6.685/www/chapter8.pdf (see page 7). The article defines this equation as: The “gap impedance”, or the impedance looking to the right from the right-most terminal of X1 is:

$$Z_g=jX_m||(jX_2+\frac{R_2}{s})$$

What do the double vertical bars mean in this context?

Hunter Livesay
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1 Answers1

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This is standard notation in electrical engineering, used for parallel impedances. It can be defined as

$$X\ ||\ Y \triangleq\frac{1}{\frac{1}{X}+\frac{1}{Y}}$$

In other words, if you have an \$X\ Ω\$ resistor in parallel with a \$Y\ Ω\$ resistor, the equivalent resistance of the two will be \$X\ ||\ Y\ Ω\$.

Hearth
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