Can I Use A Relay Wired Like This For Lights?

The picture shows the switch between the 87 and the light. Is it OK to wire a relay this way? If not, why?

If you're asking for permission, then yes, you may.

Seriously though, while you can- it would defeat the purpose of the relay. Switching either terminal 85 or 86 is your best bet.

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My ex once told me I have a perfect face for radio.

I'm re-wiring the interior light and there is already a switch on the light. I don't know how else to wire it without extra wires going from 12v source to light switch back to 85 or 86, then from 87 to light. The reason I'm asking is because after wiring it up my way my battery went caput. It was old. I have a new battery, but am reluctant to power up the relay.

Wiring it as in the picture keeps the relay energized all the time, which drains the battery. If you want to use a relay, extend the wires from the switch to either 85 or 86.

https://www.the12volt.com/relays/spdt-and-spst-automotive-relays.asp

A relay would only be necessary if the current draw was more than the switch (and wiring) could handle. If the switch is rated to handle the current draw of the interior lights, there's no need for the relay.

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My ex once told me I have a perfect face for radio.

Thank you. My suspicions were right about the relay draining the battery. I'm going to remove the relay. I don't think it needs it. Thank you explaining it to me.