Current measured by the ammeter $$(A)$$ in the reported circuit when no current flows through $$10\Omega$$ resistance, will be ______ A.

step 1: use bridge balance condition

If no current flows through the 10 Ω resistor, then the bridge is balanced:

R / 4 = 3 / 6

So,

R / 4 = 1/2
R = 2 Ω

step 2: now remove the middle branch

Since no current flows through 10 Ω, we can ignore it.

Now we have two branches in parallel:

Top branch: R + 4 = 2 + 4 = 6 Ω
Bottom branch: 3 + 6 = 9 Ω

step 3: equivalent resistance

$$R_{eq}=(6\times9)/(6+9)=54/15=3.6Ω$$

step 4: total current

$$I=V/R=36/3.6=10A$$