The figure shows part of a circuit. Three of the resistances are: R1-54 Ohms, R2

Question

The figure shows part of a circuit. Three of the resistances are: R1-54 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.) Ri^ Ra R2R

Explanation / Answer

The circuit segment is identical to wheatstone bridge network.

So , for zero current in wire ab the condition will be

R4/R3= R2/R1

R4= R3*(R2/R1)

R4=16*(80/54)

R4=23.704

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