Transfer function of this simple circuit

1. The problem statement, all variables and given/known data

The picture of the circuit is attached; I want to find [itex]|V_{A}/V_{J}|[/itex]. This seems really easy but I haven’t done circuit analysis in forever.

2. Relevant equations

Complex impedances, [itex]Z_{C} = 1/i\omega C, Z_{R} = R[/itex].

3. The attempt at a solution

First [itex]R_{A}[/itex] and [itex]C_{A}[/itex] are in parallel, so the equivalent impedance is [itex]Z_{A} = Z_{C_{A}} Z_{R_{A}} /(Z_{C_{A}} + Z_{R_{A}})[/itex]. Then the circuit is a voltage divider, so the voltage across [itex]Z_{A}[/itex] is [itex]V_{A} = V_{J} Z_{A}/(Z_{A} + Z_{R_{J}})[/itex]. Therefore,

\frac{V_{A}}{V_{J}} = \frac{Z_{A}}{Z_{A} + Z_{R_{J}}} = \frac{i R_{A}}{i(R_{A} + R_{J}) – C_{A} R_{A} R_{J} \omega} \implies \left| \frac{V_{A}}{V_{J}} \right| = \frac{R_{A}}{\sqrt{(R_{A} + R_{J})^2 + (C_{A} R_{A} R_{J} \omega)^2}}

Attached Images
File Type: png circuit.png (17.8 KB)

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