In the circuit in the figure Figure 1 a 20ohm resistor sits

In the circuit in the figure, (Figure 1) a 20-ohm resistor sits inside 110 g of pure water that is surrounded by insulating Styrofoam. If the water is initially at temperature 10.8 degree C, how long will it take for its temperature to rise to 58.9 degree C? Use 4190 J/kg middot C^n as the heat capacity of water, and express your answer in seconds using three significant figures.

Solution

Equivalent resistance of the parallel network = 20||20||10 = 10||10=5

So the equivalent resistance of whole network = 20+5+5=30 ohm

Current in 20ohm resistor = 30/30=1A

Power in 20ohm resistor = I^2*R = 1^2*20=20W

Heat required by water = mC*(T2-T1) = 0.110*4190*(58.9-10.8)=22169.29J

time = heat/power = 22169.29/20=1108.46seconds