EK #853-855

[mtravis2190]

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Hello everyone!

Questions 853-855 in examkrackers on page 91 show three different circuits. The first is just one bulb, the second shows two bulbs in series, and the third displays two bulbs connected in parallel. The battery in each circuit has the same EMF.
Questions-
853. Which of the three has the greatest current or do they all have the same current?
854. Which of the three circuits provides the most light? 855. the least light? or do they all provide the same light?

I'm having a difficult time with this one because I'm thinking that the only way to proceed with this is by being given actual values of resistance for each of the resistors. How can we solve this conceptually? Because won't there be cases depending on how we choose numbers to each of the bulbs where sometimes the series circuit or single bulb circuit may have a higher effective resistance than the parallel circuit or vice versa?

Please help! Look forward to hearing from you guys!

 

[bjc6]

Question #853

Because the EMF is constant throughout the three circuits, we can just look at the relationship between I and R. The current (I) is inversely proportional to the Resistance. So to find the greatest current we must find the smallest resistance.

For Circuit X: Rtotal = R1

For Circuit Y: Rtotal = R1 + R2

For Circuit Z: Rtotal = 1/R1 + 1/R2

So circuit Z is going to have the greatest current

Question #854

What circuit provides the most light is based on the the circuit that has the greatest power.

P= (I^2)R ; therefore since we determined in the last question that the circuit with the greatest current is Z, then then it should have the greatest power.

Question #855

The circuit with the least light would be the circuit Y because of the same reasoning as the above question. It has the greatest amount of resistance.


For these questions knowledge of the V=IR and P=(I^2)R are very important concepts. Know how the variables are related and you should do well. Good luck in your studying! You will do great!

 

[patrickmbyrne]

Basically what bjc6 said. I=V/R series will increase R and DECREASE I. Parallel will decrease R. i.e. R||R = R/2 thus increasing I. Also P=VI=(I^2)(R)=(V^2)/R=J/S=C/s*J/C=N*M/S=Kg*(M^2)/(S^2)

 

[mtravis2190]

As for the relationships between the variables in P=I^2R or P=V^2/R or P=IV, I have often been confused about what the relationship is between P and R for instance or P and V because the three equivalent formulae don't demonstrate a consistent relationship to me at first glance. I'm guessing it requires a little in depth thinking, but I don't really even know where to start. For example, are power and resistance directly proportional or inversely?

 

[mtravis2190]

Basically what bjc6 said. I=V/R series will increase R and DECREASE I. Parallel will decrease R. i.e. R||R = R/2 thus increasing I. Also P=VI=(I^2)(R)=(V^2)/R=J/S=C/s*J/C=N*M/S=Kg*(M^2)/(S^2)

As for the relationships between the variables in P=I^2R or P=V^2/R or P=IV, I have often been confused about what the relationship is between P and R for instance or P and V because the three equivalent formulae don't demonstrate a consistent relationship to me at first glance. I'm guessing it requires a little in depth thinking, but I don't really even know where to start. For example, are power and resistance directly proportional or inversely?

 

[patrickmbyrne]

As for the relationships between the variables in P=I^2R or P=V^2/R or P=IV, I have often been confused about what the relationship is between P and R for instance or P and V because the three equivalent formulae don't demonstrate a consistent relationship to me at first glance. I'm guessing it requires a little in depth thinking, but I don't really even know where to start. For example, are power and resistance directly proportional or inversely?

Ok, so from Ohm's law. (1) V=RI (2) V/R=I then (3) P=VI (1) and (3) or (2) and (3) . Then P=(I^2)R or P=(V^2)/R. If both of these relationships exist simultaneously then power is not directly proportional or inversely proportional to resistance. It is sort of a sweet spot thing. Which can be seen from the graph of power vs. resistance for the circuit given. I could go into derivations and Thevenin's theorem and max power etc.

 

[mtravis2190]

Ok, so from Ohm's law. (1) V=RI (2) V/R=I then (3) P=VI (1) and (3) or (2) and (3) . Then P=(I^2)R or P=(V^2)/R. If both of these relationships exist simultaneously then power is not directly proportional or inversely proportional to resistance. It is sort of a sweet spot thing. Which can be seen from the graph of power vs. resistance for the circuit given. I could go into derivations and Thevenin's theorem and max power etc.

Hmmm...I think I get what you're saying. For MCAT purposes, is that all I would need to know? That's what I'm most worried about. Is there any way to outline the relationships among P, I, V, and R by still avoiding any crazy calculus? I still have nightmares from first year calculus...lol!