The resistor in the heating/air conditioning system controls the blower speed. As the fan speed switch is turned, the resistor adjusts the amount of current to the blower motor, changing the fan speed.
The power dissipated by a resistor is E2/R .If the "25volt" is the potential difference (voltage) between the ends ofthe resistor, then the resistor dissipatesE2/R = (25)2/10 = 62.5 watts .That's quite a fair amount of power ... more than you could expect to dissipatefrom a typical carbon composition resistor. This particular resistor is somethinglike a heating coil in a toaster or a large acquarium, for example.
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