Question

An electric heating element to dissipate 480 watts on 240V mains is to be made from Nichromeribbon 1mm wide and thickness of 0.05mm. Calculate the length of the ribbon required if the resistivity of Nichrome is 1.1x10-6Ωm.

Answer 1

Answer:

length of the ribbon required = 5.45 m

Explanation:

Power = V²/R

=> 480 = 240²/R

=> R = 120 Ω

R = ρ L/A

A = 0.05/1000 * 1/1000  = 5 * 10⁻⁸  m²

L = ?

120 = 1.1x10 ⁻⁶ *L /5 * 10⁻⁸

=> 6 * 10⁻⁶ = 1.1x10 ⁻⁶ *L

=> L = 6/1.1

=> L = 5.45 m

length of the ribbon required = 5.45 m

Answer 2

Length of  Nichrome ribbon is 5.45 meters

Explanation:

Given as :

The power dissipated by heating element = p = 480 watts

The supply voltage from mains = v = 240 volt

The width of Nichrome ribbon = w = 1 mm = 0.001 m

The thickness of ribbon = t = 0.05 mm = 0.00005 m

The resistivity of Nichrome = $\rho$ = 1.1 × $10^{-6}$ m

Let The length of ribbon = l m

According to question

∵  power = $\dfrac{voltage^{2} }{resistance}$

i.e  p = $\dfrac{v^{2} }{r}$

Or,  r = $\dfrac{240^{2} }{480}$

∴    resistance = r = 120 ohm

Again

∵ Resistance = $\dfrac{resistivity\times length}{area}$

And Area = width × thickness

So,   A =  0.001 m × 0.00005 m

i.e   A = 5 × $10^{-8}$ m²

So,  R =$\dfrac{\rho \times l}{A}$

Or,  l = $\dfrac{R \times A}{\rho }$

Or,   l = $\dfrac{120 \times 5\times 10^{-8}}{1.1\times 10^{-6} }$

∴     l = 5.45 meters

So, The length of ribbon = l = 5.45 meters

Hence, Length of  Nichrome ribbon is 5.45 meters  Answer