When two electrical resistors with resistance R1 >0 and R2 >0 are tried in paral

Question

When two electrical resistors with resistance R1 >0 and R2 >0 are tried in parallel in a circuit, as shown in the figure to the right, the combined resistance R is given by 1/R =1/R1+1/R2.complete parts a. through d. below. a. Estimate the change in R if R1 increases from 2 ohms to 2.05 ohms and R2 decreases from 3 ohms to 2.95 ohms. The approximate change in R is . (Type an integer or a decimal) b. Is it true that if R1 =R2 and R1 increases by the same small amount as R2 decreases, then R is approximately unchanged? Explain. A. No. R is only approximately unchanged if R1=R2= 0. B. No. If R1=R2, and dR2 =-dR1, then dR=R2^2-dR1/R2^2+1 + R2^2+dR1/R2^2+1=2R2^2/R2^2+1. C Yes. If R1= R2, and dR2= -dR1, then dR=1/2(dR1? dR1) = 0. D. Yes. If R1 increases as the same rate that R2 decreases, then dR= 0 regardless of the initial values of R1 and R2.

Explanation / Answer

becoz 1/R = 1/R1 + 1/R2.

taking derivative dR/R2 = d(R1)/R12 + d(R2)/R22

so if now R = R1/2 = R2/2 becoz R1 = R2

so dR = (dR1-dR2)/2 so if dR1 = dR2 then dR = 0

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.