Question

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

• A. 0.75A
• B. 1A
• C. 2A
• D. 1.5A

Answer 1

Answer: (B)

Required arrangement is shown in figure.

The equivalent circuit will look like (since the two resistances 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 is
$\frac{(1+2) \times 3}{(1+2)+3}=\frac{3}{2} \Omega$

$\therefore $ Current in the circuit,
$I=\frac{3}{(3 / 2)}=2\, A$
$\therefore $ Current in $3 \,\Omega$ resistor $=\frac{I}{2}$
$=1 \,A$