Understanding circuits: resistance, current, and power

[combatwombat]

The circuit shown in the attached image has 3 resistors connected in parallel to a battery. If a 4th resistor is added:

A. The voltage produced by the battery will be increased
B. The voltage produced by the battery will be decreased
C. The current produced by the battery will be decreased
D. The power produced by the battery will be increased

Answer is D. I got this right, but only by eliminating A-C. I'm not seeing how power would increase. Going by P=(I^2)(R), it would actually seem that power would increase with resistance. Am I interpreting this formula the wrong way?

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[loveoforganic]

oops

 

[physics junkie]

Way too tired to give you a full blown explanation but look at how current will change. How is I calculated? It certainly won't stay the same when you add another resistor.

Ugh, I suppose I'll go a bit further but I'm not doing any equations!

V=IR. Voltage on the loop is always constant, right? Of course, it's a potential.

When you add new resistors in parallel you decrease the total resistance.

Thus to maintain constant voltage 'V' you have to increase current. So current increases by the same factor that R decreases.
Say you multiply R by 3/4 then you multiply current by 4/3 to keep V over the circuit constant.

Ok, now P=I^2*R. If you decrease resistance by (3/4) and you're squaring current (4/3) then you are really multiplying by the following: (3/4)(4/3)(4/3)...there is no way for the power to decrease.

With series it is the opposite and easier to see. P=I*V (the equations are equivalent). Let's say you have 1 resistor in series and add a 2nd. Since I=V/R and you doubled the resistance you now have I=V/2R...so your power is P=IV/2 -- it decreased by half.

This explanation sucks but its correct. You can work out the details now.

 

[combatwombat]

This explanation sucks but its correct. You can work out the details now.

Made perfect sense to me! thx

 

[physics junkie]

Made perfect sense to me! thx

You're welcome. I recommend actually calculating out adding a 3rd resistor in to a 2 resistors in parallel(easier that way than 4->5) and seeing how it changes. Knowing how to calculate it is more important than the answer. My explanation probably wouldn't get you through another question on the same diagram setup but asking you to solve for some other quantity.