A balanced bridge is shown in the circuit diagram. The metre bridge wire has resistance \(1 \Omega \mathrm{cm}^{-1}\). The current drawn from the battery is (Internal resistance of battery is negligible)

Wire has a resistance \(1 \Omega \mathrm{cm}^{-1}\).
\(\therefore\) Resistance of \(40 \mathrm{~cm}\) of wire \(=40 \Omega\)
and resistance of \(60 \mathrm{~cm}\) of wire \(=60 \Omega\)
No current flows through the galvanometer since the bridge in balanced. Hence the branch containing the galvanometer can be removed.
For balanced bridge \(\frac{4}{40}=\frac{Y}{60}\)
\(
\therefore \mathrm{Y}=\frac{4 \times 60}{40}=6 \Omega
\)
\(4 \Omega\) and \(6 \Omega\) are in series. Their equivalent resistance is \(10 \Omega\). \(40 \Omega\) and \(60 \Omega\) are in series. Their equivalent resistance is \(100 \Omega\). \(10 \Omega\) and \(100 \Omega\) are in parallel Their equivalent resistance is \(\frac{1000}{110} \Omega\).
\(\therefore\) The current \(I=\frac{\mathrm{V}}{\mathrm{R}}=\frac{6 \times 110}{1000}=0.66 \mathrm{~A}\)