Question

A variable resistor $R$ is wired into a circuit as shown below. To what value should this variable resistor be set to generate $0.9A$ of current passing through the $10$ ohm resistor?

• A. $\frac{20}{3}$
• B. $\frac{3}{20}$
• C. $\frac{1}{6}$
• D. $4$

Answer 1

The correct option is D $4$

As $0.9A$ current is passing through $10$ ohm resistor, voltage across it
$V^{\prime }=I^{\prime }{R}^{\prime }=0.9\times 10=9V$
Now $15$ ohm resistor is parallel to $10$ ohm resistor, so voltage across it will also be $9V$
Current in $15$ ohm resistor,
$I^{\prime \prime }=V^{\prime }/15=9/15=0.6A$
Total current in circuit
$I=I^{\prime }+I^{\prime \prime }=0.9+0.6=1.5A$ ,
This total current $I$ is flowing through the variable resistor $R$. Now by Kirchhoff's law in closed mesh, having variable resistor $R$ and $10$ ohm resistor
$V=10I^{\prime }+IR$
or $15=10\times 0.9+1.5R$
or $15=9+1.5R$
or $1.5R=15-9=6$
or $R=6/1.5=4\Omega$