Question

For what value of $R$(in ohms) in circuit, current through $4\Omega$ resistance is zero?

• A. $2\Omega$
• B. $1\Omega$
• C. $3\Omega$
• D. $10\Omega$

Answer 1

Answer: (B)

$1\Omega$

Consider two current mesh with currents $i_1$ and $i_2$ in clockwise direction as shown in figure.

Applying Kirchhoff's law

for left mesh: $4-10=R{i}_1+2(i_1-i_2)\Rightarrow R{i}_1+2(i_1-i_2)=-6....\left(1\right)$

for right mesh: $10-6=2(i_2-i_1)+4i_2\Rightarrow 6i_2-2i_1=4....\left(2\right)$

When no current through resistor $4\Omega$, current $i_2=0$

now from (2), $-2i_1=4\Rightarrow i_1=-2$

Putting $I_1=-2,i_2=0$ in (1), we get, $-2R-4=-6;-2R=-6+4=-2\Rightarrow R=1\Omega$