1. What is the following simplified product? Assume x>=0. 2\sqrt(8x^(3))(3\sqrt(10x^(4))-x\sqrt(5x^(2)))
2. In pure dielectrics, the parameter that is zero is
a) Attenuation
b) Propagation
c) Conductivity
d) Resistivit
The correct answer and explanation is:
The simplified product of the given expression is: 4×72(65−10)4x^{\frac{7}{2}}(6\sqrt{5} – \sqrt{10})
Now, I’ll provide the answer and explanation for the second question.
Answer:
(c) Conductivity
Explanation:
Pure dielectrics are insulating materials that do not allow free flow of electric charge under normal conditions. The parameter that is zero in pure dielectrics is conductivity.
1. Understanding Conductivity in Dielectrics
Conductivity (σ\sigma) is a measure of a material’s ability to conduct electric current. It is defined as the reciprocal of resistivity (ρ\rho): σ=1ρ\sigma = \frac{1}{\rho}
In conductors like metals, conductivity is high due to the presence of free electrons. However, in dielectrics (insulators), there are no free electrons to facilitate conduction, leading to zero or extremely low conductivity.
2. Why is Conductivity Zero in Pure Dielectrics?
- Lack of Free Charge Carriers: In a pure dielectric, all electrons are tightly bound to atoms or molecules, meaning there are no free electrons or mobile charge carriers available to conduct electricity.
- Large Band Gap: Dielectrics have a large energy gap between the valence and conduction bands, making it difficult for electrons to move freely under an electric field.
- No Ionic Movement: Unlike electrolytes, pure dielectrics do not contain free-moving ions that can conduct current.
3. Other Parameters in the Question
- Attenuation: This refers to the reduction of signal strength over distance and is not necessarily zero in dielectrics.
- Propagation: Wave propagation occurs in dielectrics, especially in electromagnetic waves, so it is not zero.
- Resistivity: Dielectrics have high resistivity, not zero resistivity.
Thus, the only correct answer is (c) Conductivity, which is zero in pure dielectrics.