Two electrical resistors When two electrical resistors with resistance R1 > 0 an

Question

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 (ohm), is Given by 1/R = 1/R1 + 1/R2 a. Estimate the change in R if R1 increases from 2 ohm to 2.05 ohm and R2 decreases from 3 ohm to 2.95 ohm. 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?

Explanation / Answer

a) R will decrease , In parallel R is maximum when both resistance are equal. If either one will increase, and other will decrease, the eq R will DECRESE.

b) Let R1 = 2ohm and R2 = 2 ohm

when they are equal Req= 2*2/4 = 1 ohm

New R1= 2.05 , and new R2 = 1.95

New Req = 2.05*1.95/4 = 0.999375 , which is appoximately equal to 1 ohm .SO TRUE (ans)

c)Yes R will increase , only when R1and R2 both increase. Because In parallel combination , the net resistance R is less than the smaller 1. So even if 1 of them increase, the net will besmaller than small one. SO IT WILL INCREASE WHEN BOTH R1 and R2 INCREASE.

d) R will decrease, as the smaller resistance R2decreases. So net resistance will be smaller than R2 . SO DECREASES>

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