Resistors in a Mixed Connection

Look at which resistors are in parallel or in series and summarize them. Work from "inside" to "outside". Here is an example: The expected measurement voltage is to be calculated. Therefor, you have to determine the total resistance:

Resistors in Mixed Connection 1

Step 1: R₁, R₂ and R₃ are parallel and can be combined to form a substitute response R_1,2,3.

R_1,2,3 = R₁/3 = 300 Ω / 3 = 100 Ω

Resistors in Mixed Connection 2

Step 2: You can now see that R_1,2,3 and R₄ are in series. The equivalent resistance R_1,2,3,4 can easily be determined by addition:

R_1,2,3,4 = R_1,2,3 + R₄ = 100 Ω + 150 Ω = 250 Ω

This results in the following equivalent circuit:

Resistors in Mixed Connection 3

Step 3: Now we dissolve the parallel connection of R_1,2,3,4 and R₅:

R_1,2,3,4,5   =   R_1,2,3,4  *   R₅     =  250 Ω  *  300 Ω   =  136,36 Ω
.                    R_1,2,3,4  +  R₅         250 Ω  +  300 Ω

Resistors in Mixed Connection 4

Step 4: What remains is a simple series connection. Calculating the total current which flows through R₆ is now a simple exercise:

R_t = R_1,2,3,4,5 + R₆  = 136,36 Ω  + 200 Ω = 336,36 Ω

I_t  =  I_R6   =   U   =       24 V         = 71,35 mA
.                    R_t       336,36 Ω

=> V_Measure = U_R6 * I_t    = 200 Ω  *  71,35 mA = 14,27 V