When two electrical resistors with resistance R1 > 0 and R2 > 0 are wired in par

Question

When two electrical resistors with resistance R1 > 0 and R2 > 0 are wired in para e n a circuit as shown in the gure to the right the combined resistance R measured in ohms ), s given by Complete parts a through d below = + R Ri R a. Estimate the change in R if R1 increases from 5 ohms to 5.02 ohms and R2 decreases from 6 ohms to 5.98 ohms. First determine the equation for dR. Choose the correct answer below (R1 +R2 1 R2 R2dR1 R1 dR2 1R2 R1 R2dR1 R1 dR2 The approximate change in R is (Do not round until the final answer. Then round to four decimal places as needed.) b. Is it true that if R1 2 ad R1 increases by the same small amount as R2 decreases, then R is approximately unchanged? Explain. A. Yes. If R1 = R2, and dR2--dR, then dR =-(dR1-dR1) = 0 B. No. If R1 = R2, and dR2--dR1, then dR = C. Yes. If R, increases as the same rate that R2 decreases, then dR=0 regardless of the initial values of R1 and R2 0 D. No. R is only approximately unchanged if R1-R2-0 c. Is it true that if R1 and R2 increase, then R increases? Explain. A. Yes. An increase in R1 and R2 means that dR, and dR2 are both positive, and the partial derivatives of R are always positive, so dR is positive O B. No. If R1 and R2 increase, then R only increases if R1 > R2

Explanation / Answer

a) R T = (R1 * R2) /(R1 + R2)

Here R1=5 Ohms

R2 = 6 Ohms

R total = 30 /11 = 2.7272

now when the values are changed here

R1 = 5.02 ohms

R2 = 5.98 Ohms

R total = 11/30.0196

= 0.366427267

change in resistance total = 2.360842733 ohms

the change in resistance total in the second case is quite reciprocal to the values of the first case.

so the calculation of option G specifies right

b) option c

if R1= R2 =5 Ohms

then R total = 25/10= 2.5 ohms

in the second case

R1 = R2 = 5.02

THEN R total = 10.04 ohms

c) option b,yes because product of the resistors increases in the numerator,therefore higher value is obtained

d)option c,R decreases ,because if R1 >R2 and dR1 = dR2

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