When there is a large difference in two resistor’s sizes, what useful approximations can be used when considering their series and parallel combinations? (This is a handy thing to know in circuit design!)

Series circuit approximation = R1 >> R2 then R2 ≈ 0

Parallel circuit approximation = R1 << R2 then R2 ≈ 0

Explanation:

in a series circuit, if there is a large difference between two resistors then we can omit the resistor which has low resistance because the higher value resistor dominates.

R1 >> R2 then R2 ≈ 0

in a parallel circuit, if there is a large difference between two resistors then we can omit the resistor which has high resistance because the lower value resistor dominates.

R1 << R2 then R2 ≈ 0

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2

the journeys of marquette, joliet and la salle a) new france expand.

all three of these explorers explored the midwest and the area around the great lakes, which they subsequently claimed for france.

this was a big portion of territory and expanded new france which before then only consisted of quebec province in northeastern canada