{"id":194,"date":"2009-07-27T06:18:13","date_gmt":"2009-07-27T11:18:13","guid":{"rendered":"http:\/\/www.blueraja.com\/blog2\/?p=194"},"modified":"2011-05-03T11:45:33","modified_gmt":"2011-05-03T16:45:33","slug":"do-transformers-obey-ohms-law","status":"publish","type":"post","link":"https:\/\/www.blueraja.com\/blog\/194\/do-transformers-obey-ohms-law","title":{"rendered":"Do transformers obey Ohm’s Law?"},"content":{"rendered":"

Ohm’s law gives a relation between Voltage, Current, and Resistance of circuit. Namely, V=IR, or
\n Voltage = Current x Resistance<\/span>
\n Note that this equation states that when Voltage goes up, current goes up.<\/p>\n

A transformer is used to change the voltage of an AC circuit – a 1:10 transformer increases the voltage to 10x its old value, while a 10:1 transformer decreases it to 1\/10th its old value.
\n
\n Transformer circuit-symbol<\/span>
\n
\n Real-life transformers consist of two wires wrapped around a metal pole<\/span><\/p>\n

Transformers must follow the rule
\n Voltageold<\/sub> x Currentold<\/sub> = Voltagenew<\/sub> x Currentnew<\/sub><\/span> (Power Conservation)
\n Thus as Voltagenew<\/sub> goes up (by, say, replacing the 1:10 transformer with a 1:11), Currentnew<\/sub> goes down.<\/p>\n

One equation says that current goes up<\/em> when voltage goes up, the other says that current goes down<\/em>. Does this mean that the two equations are incompatible and one must be thrown away when working with transformers? No!<\/em> The reason is that Ohm’s law applies to single circuits, while the other equation applies to how two separate circuits are related by a transformer.<\/p>\n

To see this more clearly, imagine the following thought experiment: we connect a 1 volt AC generator to a 1 ohm resistor and measure the current. By Ohm’s Law, we should get 1 ampere of current*:
\n
\n Now imagine we stuck a 1:10 transformer in the circuit, splitting our one circuit into two electrically-separate circuits. The confusion arises from the following question: does the current through the resistor go up because the voltage went up, or down because the transformer needs to conserve power?<\/p>\n


\n Treating the transformer as a 10-volt AC voltage source in the right circuit, we use Ohm’s law to see that the current through the resistor has gone up – it is now 10 amps. In order to preserve power, this means that in the left circuit our original AC power source is now drawing 100 amps<\/em> of current, 100x what it was drawing before.<\/p>\n

This is why high voltage power lines are still dangerous – it’s not that they would cause less current to flow through your body than low-voltage power lines, it’s that the current through your body would be less than the (enormous) current drawn at the lower-voltage end of the power-plant’s transformer.<\/p>\n

The most common answer to this question is "No, because transformers are non-ohmic devices." This is baloney – a transformer is nothing more than a pair of inductors, which are perfectly ohmic (ie. they obey Ohm’s law). For our purposes, an inductor can be thought of as a resistor that only resists AC current (this sort of “resistance” is called impedance<\/em>). This is why the left circuit (above diagram) still obeys Ohm’s law: the transformer acts somewhat like a resistor (due to its impedence) whose resistance goes up as the current demand of the right-circuit goes down.<\/p>\n

*As before<\/a>, when discussing AC voltage\/current, when we say 1 volt or amp we really mean 1 rms<\/a> ("average") volt or amp.<\/p>\n","protected":false},"excerpt":{"rendered":"

Ohm’s law gives a relation between Voltage, Current, and Resistance of circuit. Namely, V=IR, or Voltage = Current x Resistance Note that this equation states that when Voltage goes up, current goes up. A transformer is used to change the voltage of an AC circuit – a 1:10 transformer increases the voltage to 10x its […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"_links":{"self":[{"href":"https:\/\/www.blueraja.com\/blog\/wp-json\/wp\/v2\/posts\/194"}],"collection":[{"href":"https:\/\/www.blueraja.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.blueraja.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.blueraja.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.blueraja.com\/blog\/wp-json\/wp\/v2\/comments?post=194"}],"version-history":[{"count":6,"href":"https:\/\/www.blueraja.com\/blog\/wp-json\/wp\/v2\/posts\/194\/revisions"}],"predecessor-version":[{"id":245,"href":"https:\/\/www.blueraja.com\/blog\/wp-json\/wp\/v2\/posts\/194\/revisions\/245"}],"wp:attachment":[{"href":"https:\/\/www.blueraja.com\/blog\/wp-json\/wp\/v2\/media?parent=194"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.blueraja.com\/blog\/wp-json\/wp\/v2\/categories?post=194"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.blueraja.com\/blog\/wp-json\/wp\/v2\/tags?post=194"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}