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reduction of a symbolic expression

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Souljah44

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Hi,

Using EET I derived the following symbolic expression
C1*C2*C3*R1*[R2 + (RL //R3)] (R2 //R3//RL)

I know that the expression reduces to this
C1*C2*C3*R1*R2 (RL //R3)

I don't know where to begin to reduce my expression to get the final answer. Can anyone help me? Are they identities to apply? Please point me to any reference material that deals with this.

Thanks
 

If we have 3 resistor in parallel (R2//R3//RL) we can consider the parallel of two and then add the third. Since we know that the parallel of two resistor let's say Ra and Rb is given by

Req = Ra*Rb/(Ra+Rb)

we can decompose the original parallel as (simply let Ra = R2 and Rb = RL//R3):

(R2//R3//RL) = R2*(RL//R3)/[R2 + (RL//R3)]

Now substituting in the original expression:

C1*C2*C3*R1*[R2 + (RL //R3)] (R2 //R3//RL) = C1*C2*C3*R1*[R2 + (RL //R3)]*R2*(RL//R3)/[R2 + (RL//R3)]

Thus we can simplify [R2 + (RL//R3)] having as a result:

C1*C2*C3*R1*R2*(RL//R3)
 
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