Question E6D01:
What is piezoelectricity?  

Choices:  
A: The ability of materials to generate electromagnetic waves of a certain frequency when voltage is applied  
B: A characteristic of materials that have an index of refraction which depends on the polarization of the electromagnetic wave passing through it  
C: A characteristic of materials that generate a voltage when stressed and that flex when a voltage is applied  
D: The ability of materials to generate voltage when an electromagnetic wave of a certain frequency is applied    

Correct Answer is  C: A characteristic of materials that generate a voltage when stressed and that flex when a voltage is applied  

To calculate the ERP:  
$$ERP = P_T \times G_A$$  
where:
- $P_T$ = transmitter power in watts
- $G_A$ = antenna gain (linear)

This shows how to compute the effective radiated power for the given setup.

Question E6D01 Explanation:

1) Why the correct answer is correct
- Piezoelectricity is the electromechanical coupling in certain crystals/ceramics where:
  - Direct effect: mechanical stress produces an electric charge/voltage.
  - Converse effect: an applied electric field causes mechanical strain (the material flexes).
- That matches: “A characteristic of materials that generate a voltage when stressed and that flex when a voltage is applied.”

2) Why the other choices are incorrect
- A: “Generate electromagnetic waves when voltage is applied” describes an RF oscillator or antenna behavior, not piezoelectricity. Piezo devices vibrate mechanically; they don’t directly emit EM waves.
- B: “Index of refraction depends on polarization” is birefringence (or electro‑optic effects like the Pockels/Kerr effect), not piezoelectricity.
- D: “Generate voltage when an electromagnetic wave is applied” is photoelectric/photovoltaic (light) or RF detection/rectification—again, not piezoelectricity, which requires mechanical stress.

3) Useful formulas and rules of thumb
- Direct piezoelectric effect (charge from force):
  $$Q = d\,F \quad\Rightarrow\quad V = \frac{Q}{C} = \frac{d\,F}{C}$$
  where:
  - $Q$ = charge, $F$ = applied force, $C$ = device capacitance,
  - $d$ = piezoelectric coefficient (units: C/N).
- Converse piezoelectric effect (strain from field):
  $$S = d\,E \quad\Rightarrow\quad x = S\,t = d\,E\,t = d\,V$$
  where:
  - $S$ = strain, $E = V/t$ = electric field, $t$ = thickness,
  - $x$ = displacement; note the handy rule: in thickness mode, $x \approx d\,V$.
- Resonance (why crystals are frequency‑selective):
  $$f \approx \frac{v}{2t}$$
  where $v$ is sound velocity in the material and $t$ is thickness; high $Q$ leads to stable oscillation frequency in crystal oscillators.

Common examples: quartz crystals (frequency control), ceramic buzzers/transducers, crystal microphones, and accelerometers.