Question

A Nichrome heating element that has resistance 29.0 Ω is connected to a battery that has emf 96.0 V and internal resistance 1.3 Ω . An aluminum cup with mass 0.130 kg contains 0.200 kg of water. The heating element is placed in the water and the electrical energy dissipated in the resistance of the heating element all goes into the cup and water. The element itself has very small mass.

How much time does it take for the temperature of the cup and water to rise from 21.2 ∘C to 34.5 ∘C? (The change of the resistance of the Nichrome due to its temperature change can be neglected.)

Answer 1

Here

for the current in the circuit

I = V/(R1 +R2)

I = 96/(29 + 1.3)

I = 96/30.3 = 3.168 A

Now, let the time taken is t

Power * time = energy needed to raise temperature

3.168^2 * 29 * t = 0.130 * 900 * (34.5 - 21.2) + 0.20 * 4190 * (34.5 - 21.2)

solving for t

t = 43.6 s

the time taken is 43.6 s