Current density in a cylindrical wire of radius R is given as. The cur...
J= {J0[(x/R)-1] 0 ≤ x ≤ R/2, {J0(x/R) R/2 ≤ x ≤ R
We know that,
J=current/area
⇒ current=J Area
Current= J1A1 +J2A2
=J0{(x/R)−1}x(2πxdx)+J0 (x/R)(2πxdx)
=∫0R/2J0{(x/R)-1} x (2πxdx) + =∫0R/2J0 x 2π (x2/R)dx
= J0×2π∫0R/2 {(x2/R)−x}dx + (J0×2π/R) ∫RR/2 x2dx
⇒ i=J0×2π [(x3/3R)-(x2/2)] R/2 + (J0×2π/R) [x3/3]R2/R
⇒i=J0×2π [(R2/24)−(R2/8)]+ (J0×2π/R)[(R3/3)-(R3/24)]
=J0×2π(−2R2/24)(J0×2π/R)[7R3/24]
i =(5/12)πJ0R2
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Current density in a cylindrical wire of radius R is given as. The cur...
B) Copper is not a poor conductor.
Explanation:
- Copper is a good conductor of electricity and heat.
- It is widely used in electrical wiring, electronics, and many other applications that require the efficient flow of electricity.
- Copper has a high electrical conductivity, meaning that it allows electric current to flow easily through it.
- It also has a high thermal conductivity, meaning that it can transfer heat efficiently.
- Due to these properties, copper is considered one of the best conductors of electricity and heat among common metals.
- The high conductivity of copper is due to its atomic structure. Copper atoms have one free electron in their outermost energy level, which can move freely and carry electric charge.
- This delocalized electron cloud allows copper to conduct electricity efficiently.
- In contrast, poor conductors or insulators have tightly bound electrons that are not free to move, thus hindering the flow of electric current.
- Examples of poor conductors include cast iron, carbon, and tungsten.
- Cast iron is a relatively poor conductor compared to copper due to its microstructure, which consists of graphite flakes in an iron matrix. These graphite flakes act as barriers to the flow of electricity.
- Carbon, in its pure form, is a non-metal and a poor conductor of electricity. However, certain forms of carbon, such as graphite, can conduct electricity due to their layered structure and delocalized electrons.
- Tungsten is a metal with a relatively high electrical resistance, making it a poor conductor compared to copper. It is often used as a filament in incandescent light bulbs due to its high melting point and resistance to heat.
Current density in a cylindrical wire of radius R is given as. The cur...
I = JdA J = J.x/R (given) A = 2πx.dx I = J.x/R. 2πxdx I = 2πJ. /R. x²dx I = 2πJ. /R. |x²|(lim. R to R/2) I = 2πJ. /R. [x³/3](lim. R to R/2) I = 2πJ. /R. [(R³/3) - ({R/2}²/3)] I = 2πJ /R. 7R³/24 I = 7πJ.R²/12