Confused how to find the transfer function of a low-pass filter
simulate this circuit &ndash; Schematic created using CircuitLab

In the circuit shown, there are two elements, A and B, that have impedance. The element might be a resistor or a capacitor or even an inductor.

Lets call the impedance of element A, \$ Z_A\$, and element B, \$Z_B\$.

Now if both elements are resistors instead of talking about impedance we usually say resistance. We know we can use the handy voltage divider formula to find the output voltage V2.

$$ V2 = \frac{Z_B}{Z_A+Z_B} \cdot V1 $$

We can also use KVL to relate the voltage source to the current in the circuit.

$$ V1 = i \cdot (Z_A + Z_B) $$

This is still true even if they are not both resistors. The current flowing through each element will create a voltage drop across it due to the impedance it sees. So, we must use the appropriate impedance model for the element to get the correct answer.

For an inductor - \$ Z = j \omega L\$. We can substitue that value in to the above equations to get the expected result.
$$ V1 = i \cdot (R + j \omega L) \\ \\ V2 = \frac{R}{R+ j \omega L} \cdot V1 $$