# Circuit analysis, voltage in and voltage out

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

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

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?

• 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. – Sam Farjamirad Oct 29 '19 at 22:23

$$R_{23} = {\frac{1}{\frac{1}{R_2}+\frac{1}{R_3}}}$$ 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
$$k \approx 0.9895$$