Question

A battery of $12V$ is connected in the circuit as shown in figure. Find the magnitude of current $i$ :

• A. $1A$
• B. $2A$
• C. $3A$
  
• D. $4A$

Answer 1

The correct option is C $3A$

Let us start finding the equivalent resistances starting from right hand side oft the circuit.

$1\Omega$ and $1\Omega$ resistances are connected in series. The equivalent resistance of the combination is $2\Omega .$

This resistance is connected in parallel to a $2\Omega$ resistance. The equivalent resistance of this combination is $1\Omega$.

This resistance is connected in series with a $2\Omega$ resistance. The equivalent resistance of this combination is $3\Omega$.

This resistance is connected in parallel to a $6\Omega$ resistance. The equivalent resistance of this combination is $\frac{6\times 3}{6+3}\Omega =2\Omega$.

This resistance is connected in series with a $2\Omega$ resistance. The equivalent resistance of this combination is $4\Omega$.

This is connected to a $12V$ battery to receive current $i=\frac{12}{4}A=3A$