Electrical Instruments

For the galvanometer to show zero deflection, the potential difference across its terminals must be zero. This implies that the potential at point X must be equal to the potential at point Y. Let's assume the negative terminals of both batteries are at ground potential (0V). The potential at the positive terminal of the 2V battery is 2V relative to its negative terminal.
Thus, the potential at point Y is 2V. For zero deflection, the potential at point X must also be 2V. Point X is in a voltage divider circuit formed by the 300Ω resistor and resistor R, connected to the 12V battery. Using the voltage divider rule, the voltage across resistor R (which is the potential at point X relative to the negative terminal of the 12V battery) is given by: Where and we require for zero deflection. Substituting these values:
To solve for R, we first divide both sides by 2: Multiply both sides by : Rearrange the equation to solve for R: Therefore, the value of R for zero galvanometer deflection is . Correct Answer: (1)

For a Wheatstone bridge to be balanced, the following relation must hold:

We are given that the bridge is balanced when , and when and are interchanged, the bridge balances for .
This implies:

When and are interchanged, the relation becomes:

Now, from the first equation, we can express in terms of and :

Substitute this into the second equation:

Simplifying:

Now, solving for :

Thus, the correct answer is Option (4), .