All resistances in figure are $1 \Omega$ each. The value of current ' I ' is $\frac{\mathrm{a}}{5} \mathrm{~A}$. The value of a is ______

JEE Main · 2022 · 28 Jun 2022 · Shift 2 · Current Electricity

All resistances in figure are

1Ω

each. The value of current ' I ' is

\frac{a}{5} A

. The value of a is ______

Answer: 8

The circuit can be simplified by combining resistances. Using series and parallel combinations, the equivalent resistance is

R_{eq} = \frac{15 R}{8} = \frac{15}{8} Ω

. Applying Ohm's law with the 3V source:

I = \frac{V}{R _{eq}} = \frac{3}{\frac{15}{8}} = \frac{8}{5} A

. Since

I = \frac{a}{5}

, we have

a = 8

JEE Main · 2022 · 28 Jun 2022 · Shift 2 · Integer answer