Two resistors have resistances R(smaller) and R(larger), where R(smaller) < R(larger). When the resistors are connected in series to a 12.0-V battery, the current from the battery is 2.00 A. When the resistors are connected in parallel to the battery, the total current from the battery is 10.2 A. Determine the two resistances.

1.61ohms and 4.39ohms

Explanation:

According to ohm's law which States that the current (I) passing through a metallic conductor at constant temperature is directly proportional to the potential difference (V) across its ends. Mathematically, E = IRt where;

E is the electromotive force

I is the current

Rt is the effective resistance

Let the resistances be R and r

When the resistors are connected in series to a 12.0-V battery and the current from the battery is 2.00 A, the equation becomes;

12 = 2(R+r)

Rt = R+r (connection in series)

6 = R+r ...(1)

If the resistors are connected in parallel to the battery and the total current from the battery is 10.2 A, the equation will become;

12 = 10.2(1/R+1/r)

Since 1/Rt = 1/R+1/r (parallel connection)

Rt = R×r/R+r

12 = 10.2(Rr/R+r)

12(R+r) = 10.2Rr ... (2)

Solving equation 1 and 2 simultaneously to get the resistances. From (1), R = 6-r...(3)

Substituting equation 3 into 2 we have;

12{(6-r)+r} = 10.2(6-r)r

12(6-r+r) = 10.2(6r-r²)

72 = 10.2(6r-r²)

36 = 5.1(6r-r²)

36 = 30.6r-5.1r²

5.1r²-30.6r +36 =

r = 30.6±√30.6²-4(5.1)(36)/2(5.1)

r = 30.6±√936.36-734.4/10.2

r = 30.6±√201.96/10.2

r = 30.6±14.2/10.2

r = 44.8/10.2 and r = 16.4/10.2

r = 4.39 and 1.61ohms

Since R+r = 6

R+1.61 = 6

R = 6-1.61

R = 4.39ohms

Therefore the resistances are 1.61ohms and 4.39ohms

relativism, roughly put, is the view that truth and falsity, right and wrong, standards of reasoning, and procedures of justification are products of differing conventions and frameworks of assessment and that their authority is confined to the context giving rise to them. more precisely, “relativism” covers views which maintain that—at a high level of abstraction—at least some class of things have the properties they have (e.g., beautiful, morally good, epistemically justified) not simpliciter, but only relative to a given framework of assessment (e.g., local cultural norms, individual standards), and correspondingly, that the truth of claims attributing these properties holds only once the relevant framework of assessment is specified or supplied. relativists characteristically insist, furthermore, that if something is only relatively so, then there can be no framework-independent vantage point from which the matter of whether the thing in question is so can be established.

relativism has been, in its various guises, both one of the most popular and most reviled philosophical doctrines of our time. defenders see it as a harbinger of tolerance and the only ethical and epistemic stance worthy of the open-minded and tolerant. detractors dismiss it for its alleged incoherence and uncritical intellectual permissiveness. debates about relativism permeate the whole spectrum of philosophical sub-disciplines. from ethics to epistemology, science to religion, political theory to ontology, theories of meaning and even logic, philosophy has felt the need to respond to this heady and seemingly subversive idea. discussions of relativism often also invoke considerations relevant to the very nature and methodology of philosophy and to the division between the so-called “analytic and continental” camps in philosophy. and yet, despite a long history of debate going back to plato and an increasingly large body of writing, it is still difficult to come to an agreed definition of what, at its core, relativism is, and what philosophical import it has. this entry attempts to provide a broad account of the many ways in which “relativism” has been defined, explained, defended and criticized.

explanation:

multiple allele inheritance is traits controlled by more than 2 alleles (ex: pigeons having 3 alleles of one gene govern their feather color).