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In case of the voltage change which used the 3 terminal regulator, the electric power loss coming-out is the same as the case where it made the voltage fall with the resistor. It runs a lot of temperatures at the 3 terminal regulator itself.
The 1-A electric current flows when connecting the 5-ohms load with the 5-V output. The electric current that the input of the regulator is the almost same as the output flows. Because the input voltage is 12 V, the inputted electric power becomes 12V x 1A = 12W.
Because the output power is 5V x 1A = 5W, 7W of the difference become the heat with the regulator.
It is that the output voltage doesn't change even if the output current changes that is different from the case by the resistor.
I measured the temperature rise of the heatsink with the circuit which was made this time.
I installed the probe of the thermocouple-type thermometry receptacle at the heatsink in the condition which put the circuit in the case and measured it.
It rises to 100°C as much as the 10 minutes. When not considering the radiation, the regulator breaks. I made the 41 holes of 5 mm at the bottom and the top of the case respectively.
The upper limit with the operation ambient temperature of LM317 and LM337 is +125°C. The one which was made this time is near the limit. I thought that the heatsink which was used this time was big before the making. However, after measuring in the temperature, I found that the regulator had broken at the heatsink below this size.
The heatsink which I used this time is the following size.