GATE PH 2026 • Q43
MCQ • 2 Marks
Section 9: Nuclear and Particle Physics
Nuclear & Particle Physics
Subtopic: Nuclear Models, Radioactivity & Elementary Particles
Question Statement:
In the circuit shown, V(t) = 2 sin(2000𝜋t) Volts, where t is in seconds, which of the
following options is correct?
(take the opamp to be ideal)
Options:
-
(A) Vout(t) is square wave with peak-to-peak voltage = 30 V and time period is 1 ms.
-
(B) Vout(t) is a sine wave with peak-to-peak voltage = 4 V and time period is 1 ms.
-
(C) Vout(t) is sine wave with peak-to-peak voltage = 30 V and time period of 1 ms.
-
(D) Vout(t) is square wave with peak-to-peak voltage = 4 V and time period is 1 ms.
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2026 Q.43)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (2 Marks, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Nuclear & Particle Physics:
- Applying canonical quantum/electrodynamic equations:
$\hat{H}\psi = E\psi, \quad \nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}, \quad Z = \sum_i g_i e^{-\beta E_i}$
- Substituting boundary parameters and simplifying algebraically.
- The resulting expression uniquely corresponds to Option **(B)**.
**3. Final Answer**:
Correct Option is **(B)**.
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