Question

In the circuit element given here, if the potential at $B$, $V_B=0$, then the potentials $A$ and $D$ are given as

• A. $V_A=–1.5V,V_D=+2V$
• B. $V_A=–1.5V,V_D=+0.5V$
• C. $V_A=+1.5V,V_D=+0.5V$
• D. $V_A=+1.5V,V_D=–0.5V$

Answer 1

The correct option is D

$V_A=+1.5V,V_D=–0.5V$

Step 1: Voltage between $A$ and $B$

We know that potential difference is the work done to bring a unit positive charge from a given point on the conductor to another point on the conductor.

The resistance between the point $A$ and $B$ is

$V_{AB}=V_A–V_B$

$V_A–V_B=1x1.5V$

Given that $V_B=0$

$\therefore V_A=+1.5V$

Step 2: Voltage between $B$ and $C$

The resistance between the point $B$ and $C$ is

$V_{BC}=V_B–V_C$

$V_B–V_C=1x2.5V$

Given that $V_B=0$

$\therefore V_C=-2.5V$

Step 3: Voltage between $C$ and $D$

Given that the voltage between $C$ and $D$ is

$V_{CD}=V_C–V_D$

$V_C–V_D=-2V$

$\therefore -2.5–V_D=-2$

$\Rightarrow V_D=-0.5$

Therefore, $V_A=+1.5V,V_D=–0.5V$

Hence, the correct answer is option (D).