(a) 1154 K
(b) 1100 K
(c) 1400 K
(c) 1400 K
(d) 1127 K
Doubt by Suhani
Solution :
α=0.00125° C-1
T=27°C
R=1Ω
T'=?
R'=2Ω
We know,
α=0.00125° C-1
T=27°C
R=1Ω
T'=?
R'=2Ω
We know,
R=R₀[1+α(T-T₀)
Case I
R=R₀[1+α(T-T₀)]
1=R₀[1+α(27-0)]
1=R₀[1+α(27)] — (1)
Case II
R'=R₀[1+α(T'-T₀)
2=R₀[1+α(T'-0)
2=R₀[1+α(T')] — (2)
Dividing Equation (2) by (1)
2/1=R₀[1+α(T')]/R₀[1+α(27)]
2=[1+αT']/[1+27α]
2+54α=1+αT'
2-1=αT'-54α
1=α[T'-54]
1/α=T'-54
1/0.00125 = T'-54
100000/125 = T'-54
[100000×8]/[125×8] = T'-54
800000/1000 = T'-54
800=T'-54
800+54=T'
T'=854°C
T'=854+273
T'=1127 K
Case I
R=R₀[1+α(T-T₀)]
1=R₀[1+α(27-0)]
1=R₀[1+α(27)] — (1)
Case II
R'=R₀[1+α(T'-T₀)
2=R₀[1+α(T'-0)
2=R₀[1+α(T')] — (2)
Dividing Equation (2) by (1)
2/1=R₀[1+α(T')]/R₀[1+α(27)]
2=[1+αT']/[1+27α]
2+54α=1+αT'
2-1=αT'-54α
1=α[T'-54]
1/α=T'-54
1/0.00125 = T'-54
100000/125 = T'-54
[100000×8]/[125×8] = T'-54
800000/1000 = T'-54
800=T'-54
800+54=T'
T'=854°C
T'=854+273
T'=1127 K
Hence, (d) 1127K, would be the correct option.
