(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A circuit consists of 2 resistors, R1 and R2, connected in parallel across a battery.

Which statement is false?

(A) The greater power is produced in the smaller resistor.

(B) If you place another resistor in series with R1 and R2, you will

increase the overall resistance of the circuit.

(C) If you place another resistor in parallel with R1 and R2, you will

decrease the overall resistance of the circuit.

(D) If the battery is ideal, and you disconnect R2ʼs branch from the

circuit, the power dissipated in R1 will not change.

(E) If the battery is non-ideal, and you disconnect R2ʼs branch from the

circuit, the voltage difference across R1 will decrease.

(F) None of the above.

2. Relevant equations

P = ∆VI = (∆V^2)/R = (I^2)R

Series: R total = R1 + R2 + R3...

Parallel: 1/ R total = 1/R1 + 1/R2 + 1/R3...

3. The attempt at a solution

(A) True because P = (∆V^2)/R, and the smaller the resistor, the smaller the denominator, making the power larger.

(B)True because resistors in series are additive (R1+R2+R3... = R total), so adding one in series would just increase the circuit resistance

(C) True. I had to run some math to check this one, so I arbitrarily chose R1 = 2, R2 = 3, and the added R3 = 4:

Without the added resistor (R1 + R2)-

1/(R total) = 1/2 + 1/3 = 5/6, R total = 6/5, or 1.2 ohms

With the added resistor (R1+ R2 + R3)-

1/ (R total) = 1/2 + 1/3 + 1/4 = 13/12, R total = 12/13, or 0.92 ohms, which is obviously less than above

This is where I got confused:

(D) If you disconnect R2, then the ∆V across R1 will be greater, making its power greater, so I thought this one was false.

(E) If you disconnect R2, then the voltage difference across R1 will increase, right? That was my logic for (D) anyway... I'm not entirely sure how the battery being non-ideal fits in, but I think that for simplicity's sake, its like having another resistor (the 'internal resistance' resistor, in series with R1), and by removing R2, you are increasing the resistance across both which would increase the voltage change for both...

Any input would be great. Thanks!

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# Homework Help: Voltage/Circuits statements

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