How Does Adding a Resistor Affect Power Dissipation in a Parallel Circuit?

[Alexander2357]

Homework Statement

You have a circuit with a single resistor of resistance R connected to a battery that has zero internal resistance and has a power output of 12W. A resistor of resistance of 6R is now connected in parallel to the original resistor. How much power is now dissipated in the original resistor?

Homework Equations

Power:
$$P = iV = i^{2}R = \frac{V^{2}}{R}$$
Equivalent resistance in parallel:
$$\frac{1}{R_{eq}}=\sum_{j=1}^{n}\frac{1}{R_{j}}$$

The Attempt at a Solution

I feel that there isn't enough information in the question to get the required answer.

If the resistors are connected in parallel, then the voltage will be the same across them, but we don't know the voltage of the battery, we only know the power it produces. We also don't know what R is.

Would the power dissipated in the original resistor be changed if we added a second resistor in parallel? Shouldn't it remain the same?

From the given information, is it possible to find the power dissipated in the original resistor?

 

[NascentOxygen]

Would the power dissipated in the original resistor be changed if we added a second resistor in parallel?

No, it won't change.

Shouldn't it remain the same?

Yes.

A trick question?

 

[Alexander2357]

No, it won't change.


Yes.

A trick question?

So if it doesn't change, the question becomes:

"You have a circuit with a single resistor of resistance R connected to a battery that has zero internal resistance and has a power output of 12W. How much power is now dissipated in the original resistor?"

Is it possible to know the power dissipated in the original resistor now?

If we don't know the value of R, it shouldn't be possible, correct?

It is a multiple choice questions and one of the options is "Not enough information provided" so I will just choose that...

 

[NascentOxygen]

So if it doesn't change, the question becomes:

"You have a circuit with a single resistor of resistance R connected to a battery that has zero internal resistance and has a power output of 12W. How much power is now dissipated in the original resistor?"

Is it possible to know the power dissipated in the original resistor now?

Yes, it hasn't changed. What are the options in the question?

 

[Alexander2357]

Yes, it hasn't changed. What are the options in the question?

The other options are just numbers like 10W, 5W, etc. and there is no option for "Power doesn't changed" so I think the only option I have is "Not enough info" because I can't justify choosing the options with numbers.

 

[BvU]

Not enough information is not the right answer. Too much would be better already.
In fact there is contradicting (or at best ambiguous) information: "a battery that has zero internal resistance and has a power output of 12W" can be a good constant voltage source - in which case the power output changes when the load changes. The voltage remains the same. The zero internal resistance hints at that.

Or it can be a source with an output power regulator, in which case the voltage does change when the load changes.

In both cases there is enough information. Picking the right case is a gamble. My money is on the first one -- but I haven't seen the options to pick from...

 

[BvU]

I still haven't seen the options (like... ?). But you can ask yourself: is there any possibility of a power output less than 12 W ?

 

[NascentOxygen]

The other options are just numbers like 10W, 5W, etc.

Can you list all the options? Exactly.

 

[Alexander2357]

Can you list all the options? Exactly.

12W
6W
10W
5W
No enough info

I am starting to think that 12W is the correct answer since there is no internal resistance in the battery.

 

[NascentOxygen]

When the single resistor was connected to the battery, how many watts was that resistor dissipating?