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.. CP In the circuit in Fig. E26.19, a 20.0Ωresistor is inside 100gof pure water that is surrounded by insulating styrofoam.

If the water is initially at, how long will it take for its temperature to rise to58°C?

Short Answer

Expert verified

time required is t = 1006 s

Step by step solution

01

Step 1:About resitance in parrallel

theequivalentresistorofthecircuit
For the three branches in the circuit, each branch has two resistors in series; 80, the equivalent resistor of each branch is the
sum of the two resistors as shown by step (1) in the ?gure below.
Now, we have three resistors in parallel; Using equation 262, the equivalent resistor is given as followg
1Req=120+120+110

=15Ω

Req,1=5Ω

have three resistors in series, thus the equivalent resistor of the circuit is
Req=20+5+5=30Ω
Using Ohm‘s law, the current of the circuit is;
l=VReq=30V30Ω=1A

Sincetheresistor20Qisinseries,thesamecurrentis?owingthroughit.
From equation (25.18), the pOWer dissipated in a resistor R with current I flowing through is given by:
P=I2R
Now, we plug our values for R20 Q and I, so We get the pOWer dissipated in the resistor 20 Q:

r 20 Q:

P=12×20=20J/s
This is the rate of energy change from electic energy to thermal energy

02

Determine the time required

“’0know.fromequation17.13,theenergyrequiredtocauseatemperature
change AT of a substance of speci?c heat. I: and mass m is given by:
E=mcT
“’0 know, from equation 17.131 the energy required to cause a temperature
change AT of a substance of speci?c heat. c and mass m is given by:

For the water surrounding the resistor ‘20 52, we have

m=0.100kg,c=4190J/kg,T=48
’I‘lms, the energy e’lsferred from the registor 1.0 the water isF=20112J
Now, we lmve Llu‘e power and the total energy required L0 raise the temperature
of the water, the time rm‘luired for this process is:
t=EP=2011220=1005.6s

therefore time required is t = 1006 s

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Most popular questions from this chapter

BIO The average bulk resistivity of the human body (apart from surface resistance of the skin) is about 5.0Ω·m. The conducting path between the hands can be represented approximately as a cylinder 1.6 m long and 0.10 m in diameter. The skin resistance can be made negligible bysoaking the hands in salt water. (a) What is the resistance between the hands if the skin resistance is negligible? (b) What potential difference between thehands is needed for a lethal shock current of 100 mA ? (Note that your result shows that small potential differences produce dangerous currents when the skin is damp.) (c) With the current in part (b),what power is dissipated in the body?

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