BMAT Prep Question Analysis - Q78 & Q136
Q78 A student arranges four 6Ω resistors. How many functionally different resistors can be made if all resistors are used in each circuit configuration?
a. 3
b. 4
c. 5
d: 6
e. 7
Q136 The nuclei of a radioactive element decay into the nuclei of another element at a rate proportional to the number of nuclei in the first element.
Consider that a radioactive element X decays into another radioactive element Y, which further decays into a non-radioactive element Z.
If you start with a pure sample of element X, and a plot of the number of the nuclei of Y as a function of time (t), which of the following graphs do you expect to obtain?
Answer and Explanation
Q78 Answer: d. 6
Explanation: Because resistors in parallel and in series would give a different resistance, we can see that we can arrange the four resistors into different configurations of circuits to get six functionally different circuits.
Q136 Answer: Figure C
Explanation: Unstable nuclei disintegrate spontaneously and at random. The more un-decayed nuclei there are, the more frequently disintegrations are likely to occur.
As X decays into Y exponentially, you would expect to see an exponential decrease of X nuclei (similar to figure A); this corresponds to an exponential increase of Y as well. But since Y is also unstable and will also decay, it will undergo an exponential decay too. Thus we see figure C is the answer.
Initially when X decays into Y, Y increases, but when there is more and more Y, there is also a component of Y decay into Z (which is stable). Thus Y decreases exponentially.
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