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The short answer is you can't. The long answer is that it is possible with the appropriate tools but still involves applying an AC voltage to the input terminals and observing what happens on the output terminals, but it may not be necessary to use dangerous voltage levels to do this.

Why?

A transformer relies for its operation on a continuously varying magnetic field. The field is induced by current passing through the primary, driven by the applied AC voltage. It in turn induces current flow in the secondary coil, wound concentric to the input. This induction only happens as the magnetic field changes, and you can only get a changing magnetic field by flowing current through the input, and that can only happen by applying an AC voltage to the input. The magnitude of the output voltage is related (to a first approximation, with no secondary load) to the input by the simple ratio of the number of turns in the secondary coil divided by the number of turns in the primary times the input voltage.

This can not be tested using an Ohm meter. There are three basic kind of current flow - resistive, capacitative, and inductive. An Ohm meter can only measure resitive current flow. The other two require special meters known as L or C meters. The ideal transformer windings read pretty close to 0 Ohms resistively, so it is very difficult to tell if there are any short circuits between windings. An L meter can tell if there is in fact any magnetic capability. But the only true test is to input AC and measure the output with an AC volt meter. Or take it apart and see if it was OK (it won't bbe after you took it apart, of course!).

That said, an ohm meter will tell you if either coil is broken (open circuit). Some Transformers have one terminal of each coil tied to a common ground so an ohm test will not tell you if that is the case (OK) or if there is an umintended short between the coils (not OK).

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