# A schematic diagram includes both a parallel and a series circuit. R1 and R2 are parallel with R3. But R4 is in a series with R1. I know the...total resistance for the parallel circuit and the...

A schematic diagram includes both a parallel and a series circuit. R1 and R2 are parallel with R3. But R4 is in a series with R1. I know the...

total resistance for the parallel circuit and the total resistance for the series circuit. How would I go about adding them to find the total resistance? Would I just simply add them? I am just confused because R1 is included in both the parallel circuit and the series circuit. Sorry if this is confusing. I have a test tomorrow and need to know how to do this. Thanks!

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First, R1 and R4 are in series with each other, suppose these two form an equivalent resistor R5, then,

R5 = R1+R4

Now this R5, R3 and R3 are in parellel to each other.

Suppose these three form a equivalent resistor of R, then,

(1/R) = (1/R5) +(1/R2)+(1/R3)

(1/R) = (1/(R1+R4))+(1/R2)+(1/R3)

Multiply, Right hand side of the equation by ((R1+R4)R2R3)/((R1+R4)R2R3)

(1/R) = (R2R3+R3(R1+R4)+R2(R1+R4))/(R2R3(R1+R4))

By taking the reciprocal,

R = (R2R3(R1+R4))/(R2R3+R3(R1+R4)+R2(R1+R4))