The Wheatstone bridge is a simple yet elegant way of determining unknown resista

Question

The Wheatstone bridge is a simple yet elegant way of determining unknown resistances. A basic Wheatstone bridge circuit is shown below, where V is the applied voltage, Ri,R2,R3 are "known" resistances, R4 is the "unknown" resistance, and G is a galvanometer, which measures the flow of current through it. R1 R2 R3 R4 Let's investigate the Wheatstone bridge operation using basic dircuit analysis principles. Recall the rules for equivalent resistance when resistors are in series and in parallel, R1 + R2 + series R, R2 I. Ignore the galvanometer G and the voltage v, so the circuit looks as above. Let R1 = 40 , R2 = 20 , and R3-R4-30 . What is the equivalent resistance of: a) The upper branch? R1 R2 R3 R4 b) The lower branch? c) The combined upper and lower branches?

Explanation / Answer

The resistance in the upper branch = 40 + 20 ohms = 60 ohms

The resistance in the lower branch = 30 + 30 ohms = 60 ohms

The net resistance = 60 / 2 = 30 ohms

So, the net current is = V/ 20 Amps

The current in the upper branch = (V/20)* 30 / 60 = V/40 Amps

The current in the lower branch = (V/20)* 30 / 60 = V/40 Amps

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