How to Calculate the Mixed Resistance

How to calculate mixed resistors
cleverly Mixed resistors are also called compound resistors. Mixed resistor circuits refer to circuits containing series and parallel resistors. When calculating, add a series-related clever calculation formula to the parallel calculation formula:
the total resistance of adding resistance in series is small, greater than the largest;
the total resistance of adding resistance in parallel is small, less than the smallest.
The first sentence of the formula says that the total resistance of the series is obtained by adding the resistors in series, and emphasizes that this total resistance is very large and must exceed the largest one. The last sentence is to compare with the parallel connection, explaining that the parallel connection is due to the addition of more current branches, which reduces the total resistance and must be less than the smallest one.
Example 5 The circuit is shown in Figure 3-1 (C), calculate its total resistance.
Solution: First calculate R4,5=12÷4=3 (Ω). This resistor is then connected in series with R3, and its total resistance is R3,4,5=7+3=10 (Ω). R3, 4, 5 and R2 are connected in parallel, and the total resistance is R2, 3, 4, 5 = 10÷ = 5 (Ω). Finally, 2, 3, 4, 5 and R1 are connected in series, so the total resistance of this mixed series is RΣ = 5 + 5 = 10 (Ω).