0
$\begingroup$

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?

$\endgroup$
1
  • $\begingroup$ 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. $\endgroup$
    – user14407
    Oct 29, 2019 at 22:23

1 Answer 1

2
$\begingroup$

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

$k \approx 0.9895$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.