Question

A wire of length \(L\) and diameter \(d\) is used in a bulb. The temperature of wire is \(T\) and power radiated by the wire is \(P\). Its emissivity is (\(σ\) = Stefan's constant) (Assume that emissivity of wire material is same at all wavelength)

• A. \(\frac{P}{σT^4πdL}\)
• B. \(\frac{P}{σT^2πdL}\)
• C. \(\frac{P}{σT^2πd^2L^2}\)
• D. \(\frac{P^2}{σT^4πdL}\)

Hint:

Use the Stefan-Boltzmann law $P=e\sigma AT^4$ with the curved surface area $\pi dL$.

Answer 1

The Correct Option is A

Step 1: Check dimensions
$\sigma T^4$ is power per unit area, and $\pi dL$ is an area. So $\frac{P}{\sigma T^4\pi dL}$ is a pure number, as emissivity must be. The other options have wrong powers of $T$ or $L$.

Final Answer:
Option (A). \[ \boxed{\text{(A)}} \]