Power in Circuit: Calculating Output of 12V Supply

[nokia8650]

The designer of a heating element for the rear window of a car decides to connect six separate
heating elements together as shown in Figure 2. Each element has a resistance of 6.0Ω and the
unit is connected to a 12V dc supply having zero internal resistance. See: http://img219.imageshack.us/img219/7709/cirrg6.th.jpg

In order to calculate the power output of the cicuit, I found the current in one of the resistors (1A), and using P=(I^2)R, found the power output of each resistor to be 6W. 6*6 = 36W for total power output.

I was then asked to compare what would happen if the resistors were in series, which I found Total R = 36 ohms, therefore current = 12/36 = 1/3A. Again, using P=(I^2)R, I found the total power output to be 4 W.

My question is, are the calculations above correct, and if so, how come the output of a supply is varied by the contents of the circuit?

Thanks

 

[Doc Al]

Your calculations are correct. Realize that while the battery provides a fixed voltage, the amount of power delivered depends on the resistive load. (The maximum current that the battery can put out is limited.) This should make some sense: What about when you disconnect the circuit? Does the power keep getting drawn? (Disconnecting the circuit is the same as inserting an infinite resistor across the battery.)

 

[nokia8650]

Ah yes, thank you. So when a battery is short-circuited, is the current flowing very high (ie. towards infinity), resulting in very high power disspation?

Thanks

 

[Doc Al]

Right!