The resistance of an electrical toaster has a temperature dependence given by R ( T ) = R 0 [ 1 + α ( T − T 0 ) ] in its range of operation. At T 0 = 300 K , R = 100Ω and a t T = 500 K , R = 120

Question

The resistance of an electrical toaster has a temperature dependence given by R ( T ) = R 0 ​ [ 1 + α ( T − T 0 ​ ) ] in its range of operation. At T 0 ​ = 300 K , R = 100Ω and a t T = 500 K , R = 120Ω . 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 : Note: This question was awarded as the bonus since all options were incorrect in the exam.

TestHub · Accepted Answer

P = R V 2 ​ = R 0 ​ [ 1 + α ( T − T 0 ​ )] ( 200 ) 2 ​ T → temperature at 't' T 0 ​ = 300 K → temperature at t = 0 T − T 0 ​ = 30 500 − 300 ​ ( t ) T − T 0 ​ = 30 200 ​ t T − T 0 ​ = 3 20 t ​ α = R 0 ​ 1 ​ ( Δ T Δ R ​ ) = 100 1 ​ ( 200 20 ​ ) = K 1 0 − 3 ​ H =∈ tP d t = ∈ t 0 30 ​ 100 ( 1 + α 3 20 t ​ ) ( 200 ) 2 ​ dt = 100 200 × 200 ​ ∈ t 0 30 ​ 1 + 3 20 α ​ t dt ​ = 20 α 400 × 3 ​ ℓ n ( 1 1 + 3 20 ∝ ​ × 30 ​ ) = 60000 ℓ n ( 5 6 ​ )

Physics - Current Electricity Question with Solution | TestHub

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