Question

Figure shows a network of four resistances and three batteries. Mark the incorrect statement.

• A. The current flowing in the left loop is independent of the right loop.
• B. The current flowing in the right loop is independent of the left loop.
• C. Both $30V$ and $15V$ batteries do not produce current in the branch $CF$.
• D. Both (a) and (b)

Answer 1

The correct option is C Both $30V$ and $15V$ batteries do not produce current in the branch $CF$.

Apply Kirchhoff's law:

For left loop BCFAB, $4I_1+2I_1=30-6or6I_1=24\Rightarrow I_1=4A$

In this equation on $I_2$ term so the current flowing in the left loop is independent of the right loop.

For right loop DCFED, $1I_2+2I_2=15-6or3I_2=9\Rightarrow I_2=3A$

Here also no $I_1$ term so The current flowing in the right loop is independent of the left loop.

Net current in through $6V$ battery is: $I=I_1+I_2=4+3=7A$

Thus, the $6V$ battery is getting charged. Both $15V$ and $30V$ batteries produce current in $6V$ battery.