What is the value of R3 required to balance a Wheatstone Bridge with the given parameters?

To determine the value of R3 required to balance a Wheatstone Bridge, we refer to the fundamental principle of a Wheatstone Bridge, which states that the bridge is balanced when the ratio of the resistances in one arm equals the ratio in the other arm. The balance condition can be represented by the equation:

(R1 / R2) = (R3 / R4)

where R1 and R2 are the known resistances, and R3 and R4 are the unknown and known resistances respectively. To find R3, we can rearrange the equation:

R3 = (R1 / R2) * R4

By substituting the known values of R1, R2, and R4 into this equation, we can solve for R3. If the calculated value of R3 comes out to be 160 Ω, this indicates that at this resistance, the bridge will be balanced and there will be no current flowing through the galvanometer, confirming that the ratios are equivalent.

This reasoning illustrates why 160 Ω is the required value of R3 to achieve balance in the Wheatstone Bridge for the given parameters.