Question

A variable resistor $R$ is wired into a circuit 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. $6$
• D. $\frac{1}{6}$
• E. $4$

Answer 1

The correct option is E $4$

As 0.9A current is passing through 10ohm resistor therefore voltage across it ,

$V^{\prime }=I^{\prime }{R}^{\prime }=0.9\times 10=9V$

now 15 ohm resistor is parallel to 10 ohm resistors so voltage across it will also be of 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 10ohm 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 $R=6/1.5=4\Omega$