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An electric filament can heat 200 cm³ of water from 5°C to 95°C in 6 minutes. If the voltage source is a 12 V battery, how much current does it draw?

Answer :

The current drawn by the filament is 0.26 A.

  • The equation for calculating the amount of heat generated is given by:
  • Q = mcΔT. where. Q = heat energy required, m = mass of water (kg), c = specific heat capacity of water (4.2 kJ/kg K)Δ, T = temperature difference
  • The heat energy required to heat 200 cm³ of water from 5°C to 95°C is given by: Q = mcΔT= (0.2 kg) (4.2 kJ/kg K) (95°C - 5°C)= 33.6 kJ
  • The electrical energy consumed by the filament is equal to the heat energy generated: W = Q= 33.6 kJ
  • The time taken is 6 minutes or 360 seconds, thus:
  • W = VItdoing some rearrangements, V = W / It where V = 12 V, W = 33.6 kJ, and t = 360 s
  • Rearranging and substituting values,12 V = 33.6 kJ / I (360 s)I = 0.26 A
  • Therefore, the current drawn by the filament is 0.26 A.
  • Summary: An electric filament can heat 200 cm3 of water from 5°C to 95°C in 6 minutes. The heat energy required to heat 200 cm³ of water from 5°C to 95°C is given by: Q = mcΔT = (0.2 kg) (4.2 kJ/kg K) (95°C - 5°C) = 33.6 kJ.
  • The electrical energy consumed by the filament is equal to the heat energy generated. The current drawn by the filament is 0.26 A.

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