Question

Three resistors $1\Omega$, $2\Omega$ and $3\Omega$ are connected to form a triangle. Across $3\Omega$ resistor a $3V$ battery is connected. The current through $3\Omega$ resistor is:

• A. $0.75A$
• B. $1A$
• C. $1.5A$
• D. $2A$

Answer 1

Answer: (B)

The correct option is B $1A$
The arrangement is shown in figure.
Here, two resistance of $1\Omega$ and $2\Omega$ are in series, which form $3\Omega$ which is in parallel with $3\Omega$ resistance.
Therefore, the effective resistance
$\frac{(1+2)\times 3}{(1+2)+3}=\frac{3}{2}\Omega$
$\therefore$ Current in the circuit,
$I=\frac{3}{\left(3/2\right)}=2A$
$\therefore$ Current in $3\Omega$ resistor $=\frac{I}{2}=IA$