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I want to solve $V_o$ in terms of $V_i$ from the following circuit.

enter image description here

$R_1=95.7 \Omega, R_2=9.1 k\Omega, R_3=1.0 M\Omega$

So the solution is form $V_o=kV_i$ and I want the factor k.

I know that:

$R_{123}=R_1+R_{23}$

and $R_{23}= 9017.94$ so the $R_{123}=9113.64\Omega$

But how do I get the factor k?

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  • $\begingroup$ Calculate the equivalent resistance of $R_2$ and $R_3$, then use the voltage divider to find the factor $k$, the factor k is equal to $\frac{R_e}{R_e+R_1}$ with $R_e$ I mean the equivalent resistance of those resistors in parallel. $\endgroup$ – Sam Farjamirad Oct 29 '19 at 22:23
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$R_{23} = {\frac{1}{\frac{1}{R_2}+\frac{1}{R_3}}}$ Resistors in parallel
$R_{23} \approx 9.018KΩ$ Plugging in the values

$V_{out} = V_{in} \cdot {\frac {R_{23}}{R_{1} + R_{23}}}$ Voltage division
$V_{out} \approx 0.9895 \cdot V_{in}$ Plugging in the values

$k \approx 0.9895$

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