Question

Calculate the temperature at which the resistance of a conductor becomes 20

Answer 1

Answer:

Let be the resistance at 270oC is R.

Let the temperature be T at which resistance become 20% more(R+20R/100=6R/5).

We know

Rt=Ro⎛⎝⎜⎜⎜1+αt⎞⎠⎟⎟⎟; where α is the temprater coefficient.R270=Ro⎛⎝⎜⎜⎜1+α×270⎞⎠⎟⎟⎟=R .............⎛⎝⎜⎜⎜1⎞⎠⎟⎟⎟And Rt=Ro⎛⎝⎜⎜⎜1+αt⎞⎠⎟⎟⎟=6R5..............⎛⎝⎜⎜⎜2⎞⎠⎟⎟⎟dividing eq⎛⎝⎜⎜⎜1⎞⎠⎟⎟⎟ and ⎛⎝⎜⎜⎜2⎞⎠⎟⎟⎟, we getRo(1+α×270)Ro(1+αt)=R6R5=56⇒1+α×2701+αt=56⇒t=(6(1+α×270)5−1)α=(6(1+2×10−4×270)5−1)2×10−4=(6(1.0540)5−1)2×10−4=0.26482×10−4=1324oC