Mathematics, 11.11.2019 19:31 ruslffdr

When two electrical resistors with resistancer1> 0 andr2> 0 are wired in parallelin a circuit, the combined resistancer, measured in ohms (ω), is given by1r=1r1+1r2(a) find∂r∂r1and∂r∂r2after solving forr(e. g.,r=. ) describe how an increase inr1withr2held constant affectsr. (willrincreaseor ) describe how a decrease inr2withr1held constant affectsr. (willrincreaseor decrease? )

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Answer from: meep26wesley

$\bf \frac{\partial R}{\partial R_1}=\frac{R_2^2}{(R_1+R_2)^2}$

$\bf \frac{\partial R}{\partial R_2}=\frac{R_1^2}{(R_1+R_2)^2}$

b) and c)

See explanation below

Step-by-step explanation:

The combined resistance R is a function of the the two

parallel resistances

$\bf \frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}=\frac{R_1+R_2}{R_1R_2}$

$\bf R(R_1,R_2)=\frac{R_1R_2}{R_1+R_2}$

and we have

$\bf \frac{\partial R}{\partial R_1}=\frac{R_2(R_1+R_2)-R_1R_2}{(R_1+R_2)^2}=\frac{R_2^2}{(R_1+R_2)^2}$

Similarly,

$\bf \frac{\partial R}{\partial R_2}=\frac{R_1(R_1+R_2)-R_1R_2}{(R_1+R_2)^2}=\frac{R_1^2}{(R_1+R_2)^2}$

If we divide both the numerator and denominator by $\bf R_1$ in the expression for R, we get

$\bf R=\frac{R_2}{1+R_2/R_1}$

hence, if we held $\bf R_2$ constant and increase $\bf R_1$ the fraction $\bf \frac{R_2}{R_1}$ gets smaller and so does the denominator of R, as a consequence R gets larger.

When $\bf R_1$ is very large, the denominator of R is close to 1, so R is close to $\bf R_2$

By a symmetric reasoning, we see that R gets larger when holding $\bf R_1$ constant and $\bf R_2$ increases.

In this case, R gets closer to $\bf R_1$ as $\bf R_2$ grows.

Answer from: Quest

step-by-step explanation:

Answer from: Quest

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab in the y coordinate

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

x coordinate

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

y coordinate

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

x coordinate

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

y coordinate

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

x coordinate

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

y coordinate

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

x coordinate

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

y coordinate

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

x coordinate

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

y coordinate

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

x coordinate

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

y coordinate

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

x coordinate

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

y coordinate

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕

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When two electrical resistors with resistancer1> 0 andr2> 0 are wired in parallelin a circuit,...