Question Details

Choose the correct circuit which can achieve the bridge balance

Options

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Correct Answer :

Option A

The circuit where the diode is in series with the 5 Ω resistor and is forward-biased (with its anode connected towards the bottom junction and its cathode connected towards the right junction, so that the arrow points towards the right junction).

Solution :

To find the correct circuit that can achieve the bridge balance, we must analyze the balance condition of a Wheatstone bridge.

A Wheatstone bridge is balanced when the ratio of the resistances of the adjacent arms is equal. For a standard bridge configuration with resistors:
- Top-left arm: $R_{1} = 10 Ω$
- Top-right arm: $R_{2} = 10 Ω$
- Bottom-left arm: $R_{3} = 15 Ω$
- Bottom-right arm: $R_{4}$ (consisting of a $5 Ω$ resistor in series with a diode $D$ )

The balance condition is given by:
$\frac{R_{1}}{R_{2}}$
Substituting the given resistance values:
$\frac{10}{10} = \frac{15}{R_{4}}$
$1 = \frac{15}{R_{4}} \Rightarrow R_{4} = 15 Ω$

Since the bottom-right arm contains a $5 Ω$ resistor in series with a diode $D$ , the total resistance of this arm is:
$R_{4} = 5 + r_{d}$
where $r_{d}$ is the dynamic resistance of the diode. For the arm resistance to be $15 Ω$ :
$5 + r_{d} = 15 \Rightarrow r_{d} = 10 Ω$

For the diode to have a finite, positive dynamic resistance ( $r_{d} = 10 Ω$ ), it must be in the forward-biased state. If it were reverse-biased, its resistance would be ideally infinite, and the bridge could not be balanced.

Looking at the battery connection, the positive terminal is connected to the left junction and the negative terminal is connected to the right junction. Thus, current flows from the left junction towards the right junction.
In the bottom branch, current flows from the bottom junction to the right junction. For the diode to be forward-biased under this current flow, its anode (the triangle side of the symbol) must be connected to the bottom junction, and its cathode (the bar side of the symbol) must be connected to the right junction. Therefore, the arrow of the diode must point towards the right junction.