The Network shown in figure is a part of the circuit. (The battery has negligible resistance).

At a certain instant the current 2 A and it is decreasing at the rate of \(10^2 As ^{-1}\). What is the potential difference between the points \(B\) and \(A\) ?

A 8.0 V
B 8.5 V
C 10 V
D 15 V

Verified Solution

Answer & Solution

Correct Answer

(B) 8.5 V

Step-by-step Solution

Detailed explanation

B
As per second law of Kirchhof
\(\begin{array}{l}
V_{A}-IR+\varepsilon+L \frac{d I}{d t}=V_{B} \\
V_{B}-V_{A}=-IR+\varepsilon+L \frac{d}{d t}
\end{array}\)
\(\begin{aligned} V _{ B }- V _{ A }= & (-2 \times 2)+(12) \\ & +\left(5 \times 10^{-3} \times 10^2\right)\end{aligned}\)
\(\begin{array}{l}V_B-V_A=-4+12+0.5 \\ V_B-V_A=8.5 V\end{array}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From GUJCET

Explore more questions on app

The Network shown in figure is a part of the circuit. (The battery has negligible resistance).At a certain instant the current 2 A and it is decreasing at the rate of \(10^2 As ^{-1}\). What is the potential difference between the points \(B\) and \(A\) ?

Step-by-step Solution

The Network shown in figure is a part of the circuit. (The battery has negligible resistance).

At a certain instant the current 2 A and it is decreasing at the rate of \(10^2 As ^{-1}\). What is the potential difference between the points \(B\) and \(A\) ?