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. 1 A
• B. 2 A
• C. 1.5 A
• D. 0.75 A

Answer 1

Answer: (A)

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