In a the circuit mixes, some of the resistors are connected in series while the other is connected in parallel. To calculate the value of

**R**_{t} in series-parallel circuit, the first method is to find the groups of resistors are all connected in series or all of which are connected in parallel.

Draw back the circuit, by replacing each group of resistors into **an equivalent resistor**. Gradually, simplify the circuit to produce an R_{t}, or the resistance of a single end.

Example question:

What is the value of R_{t}, or the equivalent resistance of the circuit resistor mixture below?

Completion:

On the image above the resistance value of 56 Ω and 33 Ω are connected in parallel, then parallel connection is connected in series with 47 Ω.

Create R_{t1} equivalent resistance for parallel connection resistance 56 Ω and 33 Ω, with a parallel formula

1/R_{t} = 1/R_{1} + 1/R_{2} + 1/R_{3} + · · · + 1/R_{n}, then

1/R_{t1} = 1 / 56 + 1 / 33

1/R_{t1} = 89/1848

89R_{t1} = 1848

R_{t1} = 1848/89

R_{t1} = 20.8 Ω

Parallel connection of resistance 56 Ω and 33 Ω can be replaced with an equivalent resistance of 20.8 Ω. This simplification produces two resistance are connected in series, which is 20.8 Ω and 47 Ω.

Equivalent series resistance value according to the series formula

R_{t} = R_{1} + R_{2} + R_{3} + · · · + R_{n}, then

R_{t} = 20.8 + 47

R_{t} = 68.7 Ω

Thus obtained R_{t} or an equivalent resistance for 67.8 Ω

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