The figure shows part of a circuit. Three of the resistances are: R154 Ohms, R2

Question

The figure shows part of a circuit. Three of the resistances are: R154 Ohms, R2 80 Ohms, and R3 = 16 Ohms. You want to design this circuit so that if you connect a wire between points A and B, no current will flow through that wire. How large must R4 be in order for this to be true? Give your answer in Ohms, to at least three significant digits. You will not be graded on the number of digits, this is just to avoid rounding errors. (Note: This is, in fact, a sensitive way to measure resistance if you know R1, R2, and R3 to high accuracy.)

Explanation / Answer

here R1 and R3  and R2 and R4 are in series then

R1 and R3  = 54 + 16 = 60 ohm

and R2 and R4  = 80 + R4 0hm

now they both are in parallel so total resistance

RT = 60(80+R4) / (60 +80 +R4)

= 60(80+R4) / (140 + R4)

here there is no current flow between A and B

I = 0 = V / RT

V(140+R4) / 60(80+R4) = 0

it only possible when R4 = -140 ohm and R4 = infinity

the R4 = -140 ohm is not possible so R4 = infinity ohm Ans

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