Two electrical resistors When two electrical resistors with resistance R 1 > 0 and R 2 > 0 are wired in parallel in a circuit (see figure), the combined resistance R, measured in ohms (Ω), is given by 1 R = 1 R 1 + 1 R 2 a. Estimate the change in R if R 1 increases from 2 Ω to 2.05 Ω and R 2 decreases from 3 Ω to 2.95 Ω . b. Is it true that if R 1 = R 2 and R 1 increases by the same small amount as R 2 decreases, then R is approximately unchanged? Explain. c. Is it true that if R 1 and R 2 increase, then R increases? Explain. d. Suppose R 1 > R 2 and R 1 increases by the same small amount as R 2 decreases. Does R increase or decrease?
Two electrical resistors When two electrical resistors with resistance R 1 > 0 and R 2 > 0 are wired in parallel in a circuit (see figure), the combined resistance R, measured in ohms (Ω), is given by 1 R = 1 R 1 + 1 R 2 a. Estimate the change in R if R 1 increases from 2 Ω to 2.05 Ω and R 2 decreases from 3 Ω to 2.95 Ω . b. Is it true that if R 1 = R 2 and R 1 increases by the same small amount as R 2 decreases, then R is approximately unchanged? Explain. c. Is it true that if R 1 and R 2 increase, then R increases? Explain. d. Suppose R 1 > R 2 and R 1 increases by the same small amount as R 2 decreases. Does R increase or decrease?
Two electrical resistors When two electrical resistors with resistance R1 > 0 and R2 > 0 are wired in parallel in a circuit (see figure), the combined resistance R, measured in ohms (Ω), is given by
1
R
=
1
R
1
+
1
R
2
a. Estimate the change in R if R1 increases from 2 Ω to 2.05 Ω and R2 decreases from 3 Ω to 2.95 Ω.
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.
c. Is it true that if R1 and R2 increase, then R increases? Explain.
d. Suppose R1 > R2 and R1 increases by the same small amount as R2 decreases. Does R increase or decrease?
Thomas' Calculus: Early Transcendentals (14th Edition)
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