The resistance of an electrical toaster has a temperature dependence given by $R(T) = R_{0}[1 + \alpha(T -…

The resistance of an electrical toaster has a temperature dependence given by $R(T) = R_{0}[1 + \alpha(T - T_{0})]$ in its range of operation. At $T_{0} = 300$ K, $R = 100 \Omega$ and at $T = 500$ K, $R = 120 \Omega$. The toaster is connected to a voltage source at $200$ V and its temperature is raised at a constant rate from $300$ to $500$ K in $30$ s. The total work done in raising the temperature is:
  1. 60000 ln65  J
  2. 200 ln23 J
  3. 300 J
  4. 400 ln1.51.3 J

Solution

P= V 2 R =2002R0[1+α(T-T0)]

T → temperature at 't'

T 0 =300K → temperature at t = 0  

T - T 0 = 5 0 0 - 3 0 0 3 0 t

T - T 0 = 2 0 0 3 0 t

T - T 0 = 2 0 t 3

α=1R0∆R∆T=110020200=10-3K    

H=∫Pdt=

∫ 0 3 0 2 0 0 2 1 0 0 1 + α 2 0t 3 dt = 2 0 0 × 2 0 0 1 0 0 ∫ 0 3 0 dt 1 + 2 0 α 3 t

= 4 0 0 × 3 2 0 α ℓ n ( 1+ 20∝ 3 ×30 1 )

= 6 0 0 0 0  ℓ n  6 5

Asked in: JEE Main 2016 (10 Apr Online)

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