Each of the resistance shown in figure has a value of 20 Ω. Find the equivalent resistance between A and B. Does it depend on whether the point A or B is at higher potential?

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Solution

According to the Wheatstone bridge principle, if the bridge is balanced, then the current flow across the central resistor is zero. So, to simplify the circuit, we can remove the central resistor.
The given circuit is also balanced, so there is no current through the diode.
Hence, the net resistance of the circuit is given by
$R_{P} = \frac{R_{1} R_{2}}{R_{1} + R_{2}} For R_{1} = R_{2} = R, R_{P} = \frac{R}{2} = \frac{40}{2} \Rightarrow R_{P} = 20 Ω$

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