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Electricity

Resistors in parallel - formula in LaTeX

In a parallel connection the reciprocals add up, so the equivalent resistance is smaller than the smallest resistor. For two resistors it comes out as the product over the sum. The summation sign is \sum and the index goes in _{i}.

1Rz=∑i1Ri\dfrac{1}{R_z} = \sum_{i} \dfrac{1}{R_i}

LaTeX code

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$$
\dfrac{1}{R_z} = \sum_{i} \dfrac{1}{R_i}
$$

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What the symbols mean

RzR_z
equivalent resistance (Ω)
RiR_i
resistance of the i-th resistor (Ω)

An electricity and magnetism formula - the basis of circuit problems and electrical lab reports.

Worked example

A 6 Ω and a 3 Ω resistor in parallel. For two resistors R₁R₂/(R₁ + R₂) = 18/9 Ω gives the same result, and the equivalent resistance is always smaller than the smallest one.

1Rz=16 Ω+13 Ω=12 Ω⇒Rz=2 Ω\dfrac{1}{R_z} = \dfrac{1}{6\,\Omega} + \dfrac{1}{3\,\Omega} = \dfrac{1}{2\,\Omega} \quad\Rightarrow\quad R_z = 2\,\Omega

LaTeX commands in this formula

\dfrac
fraction (display)
x_{0}
subscript; wrap several characters in braces
\sum
sum

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