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Hello. I've been doing problems, and transforming from time domain to phasor domain to find input impedances seems simple enough But I've come across a circuit with a dependent voltage source, as shown in the above figure, and I'm not sure how to approach it. Must a voltage be assumed?

With the assumption, a voltage across the 5ohm resistor is obtained as well as the dependent source. But does that make the value in the dependent source an impedance as well? Thank you for your time.

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The usual way to find a Thevenin equivalent for a circuit with dependent sources is to connect a 1 amp test source to the input. Find the voltage across the terminals, then divide by 1 amp to get the Thevenin impedance:

$$R_{th} = \frac{v_{in}}{1\ A}$$

The Thevenin voltage is found in the usual way, by determining the open-circuit voltage \$v_{in}\$. Without an independent source, the dependent source is inactive. (No current means \$v = 0\ V\$). So the open-circuit voltage is 0 V. The Thevenin equivalent is just an impedance.

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