Can you please help me with this? The cohises for C & D are (increase , decrease

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Can you please help me with this?

The cohises for C & D are (increase , decrease)

The cohises for C & D are (increase , decrease)

Two resistors in an electrical circuit with resistance R1 and R2 wired in parallel with a constant voltage give an effective resistance of R, where 1/R = 1/R1 + 1/R2. Complete parts (a) through (d). Find R/ R1 by solving for R and differentiating. Choose the correct answer below. Describe how an increase in R1 with R2 constant affects R. As R1 increases with R2 constant, R Describe how a decrease in R2 with R1 constant affects R. As R2 decreases with R1 constant, R

Explanation / Answer

1)

R = R1R2/(R1+R2)

-> dR/dR1 = (R2 (R1+R2) - R1R2)/(R1+R2)^2 = (R2/(R1+R2))^2

answer B.

2)

-> dR/dR2 = (R1 (R1+R2) - R1R2)/(R1+R2)^2 = (R1/(R1+R2))^2

answer D.

3)

implicitly:

1/R = 1/R1 + 1/R2 -> -1/R^2 dR = -1/R1^2 dR1 + 0 -> dR/dR1 = R^2/R1^2 = (1/R1 + 1/R2)^2/R1^2 =

R2^2/(R1+R2)^2

4)

implicitly:

1/R = 1/R1 + 1/R2 -> -1/R^2 dR = 0 -1/R2^2 dR2 -> dR/dR2 = R^2/R2^2 = (1/R1 + 1/R2)^2/R2^2 =

R1^2/(R1+R2)^2

c)

since dR/dR1 and dR/dR2 are positive, increasing R1 and R2, will increase R.

d)

since dR/dR1 and dR/dR2 are positive, decreasing R1 and R2, will decrease R.

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