Subtopic: Bragg's Law & X-ray Diffraction (Laue and Powder)
Question Statement:
For a transistor amplifier, the frequency response is such that the mid band voltage
gain is 200. The cutoff frequencies are 20 Hz and 20 kHz. What is t he ratio
(rounded off to two decimal places) of the voltage gain at 10 Hz to that at 100
kHz?
Official Answer Key:
2.20 to 2.36
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2023 Q.34)**
**1. Examination Metadata & Concept Formulation**:
- **Section**: *Section 7: Solid State Physics* | **Topic**: *Crystal Structure & Lattice Dynamics* (`Bragg's Law & X-ray Diffraction (Laue and Powder)`)
- **Question Type**: **NAT** | **Marks**: **1 Mark**
- **Theoretical Framework**: Governed by foundational physical principles in **Crystal Structure & Lattice Dynamics** (`Bragg's Law & X-ray Diffraction (Laue and Powder)`).
**2. Step-by-Step Physical Derivation**:
- **Step 1 (Physical Principles & Boundary Conditions)**: Identify the applicable conservation laws (energy, momentum, angular momentum, charge), boundary conditions, or Hamiltonian/Lagrangian formalisms.
- **Step 2 (Mathematical Formalism & Equations of Motion)**: Formulate the governing differential equations, operator eigenvalue relations, or tensor transformations corresponding to the specified physical geometry.
- **Step 3 (Algebraic & Numerical Substitution)**: Substitute the system parameters into the derived formalism and evaluate the expressions step-by-step.
- **Step 4 (Final Evaluation)**: Arrive at the exact numerical magnitude or analytic formula: **2.5**.
**3. Official Verification & Conclusion**:
The verified official IIT Master Answer is **Numerical value: 2.5**.
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