P 4.3-8 The circuit shown in Figure P 4.3-8 has two inputs, v1 and v2, and one output, vo. The output is related to the input by the equation

where a and b are constants that depend on R1, R2 and R3.

(a) Determine the values of the coefficients a and b when R1 = 10 Ω, R2 = 40 Ω and R3 = 8 Ω.

(b) Determine the values of the coefficients a and b when R1 = R2 and R3 = R1 || R2.

 

Figure P 4.3-8

 

(a) Determine the values of the coefficients a and b when R1 = 10 Ω, R2 = 40 Ω and R3 = 8 Ω.

 

Our circuit now looks like

Write out node equation for v0

Find common denominator

 

Multiply by 40 Ω and isolate v0

 

 

 

So

 

(b) Determine the values of the coefficients a and b when R1 = R2 and R3 = R1 || R2.

 

So if R3 is the equivalent of R1 and R2 in parallel, since R1 = R2, in parallel the equivalence would be R1/2.  Consider R1 = R.  So our circuit now looks like

Write out node equation for v0

Find common denominator

 

 

Multiply by R and isolate v0

 

 

 

So

 

For Part (a)

For Part (b)

 

 

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This page last updated on January 30, 2019