How do I use Thevenin's theorem to determine the values of the Thevenin equivalent on the right? Vth=? Rth=?

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RTH is the resistance measured at terminals with all voltage sources replaced by short circuits and all current sources replaced by open circuits. Since in this case you only have a voltage source, you just short that out.

Shorting the source the, resistances are in parallel connection. `R_1 = 15...

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RTH is the resistance measured at terminals with all voltage sources replaced by short circuits and all current sources replaced by open circuits. Since in this case you only have a voltage source, you just short that out.

Shorting the source the, resistances are in parallel connection.
`R_1 = 15 ohms` 
`R_2 = 30 ohms` 
`V = 15 V`

`RTH = (R_1(R_2))/(R_1+R_2)`

`RTH = (15*30)/(15+30)`

`RTH = 450/45`

`RTH = 10 ohms`

VTH is voltage seen at the terminals. You can use voltage divider:

`VTH = (V * R_2)/(R_1+R_2)`

`VTH = (15*30)/(15+30)`

`VTH = 450/45`

`VTH = 10 V`


Thus, RTH = 10 ohms and VTH = 10 volts.

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