Question

When the bridge shown is balanced, the current through the resistor $R_a$ is________ mA (rounded off to two decimal places). The bridge has $R_a=R_b=R_c=10~\mathrm{m}\Omega$ and the detector (galvanometer) is ideal/open at balance; the source is $1~\text{V}$.

Hint:

In a balanced (null) bridge, the detector branch is open—use symmetry/equal–ratio arms to read currents directly in identical branches.

Answer 1

Correct Answer: 0.99

Balance condition. At balance the detector carries no current, so the two vertical arms with $R_a$ and $R_b$ are at the same potential at their junctions; consequently $R_c$ has no net drop and the currents in the two arms are equal.
[2mm] Current through $R_a$. With symmetry and equal low–value arms, the excitation divides equally between the two identical branches, giving the same current through $R_a$ and $R_b$. This evaluates to \[ I_{R_a}=1.00~\text{mA}\;(\text{rounded to two decimals}). \]