Question

In the circuit shown the variable resistor X is adjusted so that high resistance voltmeter V shows a reading of 1 V. The resistance, then is

• A. 1.5 $\Omega$
• B. 50 $\Omega$
• C. 3.0 $\Omega$
• D. 2.5 $\Omega$

Answer 1

Answer: (A)

1.5 $\Omega$

In the upper loop.
Through 5 V,
$V_A+2i-5=V_B$, suppose $i$ is the current through the circuit.
$\therefore V_A-V_B=5-2i=1$
$\therefore i=\frac{5-1}{2}=2A$
In the lower loop.
Through 2V,
$V_A+2-iX=V_B$
$\Rightarrow iX=V_A-V_B+2$
But $V_A-V_B=1$ volt$,i=2$ A
$\Rightarrow X=\frac{1+2}{2}=1.5\Omega$