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Complicated resistor networks can often be simplified into a single equivalent resistor value. Two equations used in the simplification process are the resistors in series equation and the resistors in parallel equation.

Resistors are in series when chained together in a single line. The current flowing is common to all resistors in this chain. This is because the current flowing through the first resistor has one path through each of the following resistors in the chain. The total resistance of must equal the sum of each resistor’s value used in the chain.

We can consider this entire chain of resistors as a single resistor with a value of ~R_{\text{equiv}}~.

Resistors are in parallel when they share the same two nodes. The voltage drop across each resistor in this configuration is common. The current now has multiple paths and may not be the same for each resistor. The total resistance of resistors in parallel is the sum of the reciprocal of each resistor’s value used.

We can consider these parallel resistors as a single resistor with a value of ~R_{\text{equiv}}~