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A Niehrome heating element that has resistance 28.0 ? is
Chapter 25, Problem 61P(choose chapter or problem)
A Nichrome heating element that has resistance \(28.0\ \Omega\) is connected to a battery that has emf 96.0 V and internal resistance \(1.2\ \Omega\). 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 \(21.2^{\circ} \mathrm{C} \text { to } 34.5^{\circ} \mathrm{C}\)? (The change of the resistance of the Nichrome due to its temperature change can be neglected.)
Text Transcription:
28.0 Omega
1.2 Omega
21.2^circ C to 34.5^circ C
Questions & Answers
QUESTION:
A Nichrome heating element that has resistance \(28.0\ \Omega\) is connected to a battery that has emf 96.0 V and internal resistance \(1.2\ \Omega\). 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 \(21.2^{\circ} \mathrm{C} \text { to } 34.5^{\circ} \mathrm{C}\)? (The change of the resistance of the Nichrome due to its temperature change can be neglected.)
Text Transcription:
28.0 Omega
1.2 Omega
21.2^circ C to 34.5^circ C
ANSWER:Solution 61P
Step 1:
Current through the circuit
I = ………….(1)
Resistance of the heating element R =28
Resistance of the aluminium chamber r= 1.2
emf of the battery, v =96v
Put these values in equation (1)
I = = 3.288A
The electric power , P =I2 R
P = (3.288)2 28 = 301.70