Question

Problem I-B Circuit shown below in Fig. 1-B is used to heat water (of 5000 American gallon) illustrated. A DC voltage source of 120 volts is used to energize three heating elements, each of value (3R) ohm. It is observed that the temperature of the water changes from 100° F to 200° F over a time period of 1.5 hours. Calculate as (i) Total current supplied by the de source at 100°F (Ans: 12.47 A) Resistance value (R in ohm) of cach heating element at 200 F (Ans: 35 ohm) (ii) (iii) Rating of each heating element (iv) Is there any engineering advantage of the arrangement of three heating elements configured as shown in Fig. 1? Explain Specific heat of water Specific heat capacity of water: 4,185.8 joules per kilogram per degree celsius (J/kg°C); calorie 4.1858 joule; Temperature coefficient of resistivity of the heating element, a- 0.004/C; 1 American gallon 3.8 liters. FIG. I-B 100 3R Problem II-B

Answer 1

Assume the heater heats 5gallons to obtain correct answers.

rating of each element is found to be approximately 500W as mentioned at the end of first page.
arvangement u to ioorease the overall the pesistamce Cegeuierlent) and inceasing The aim 6 buh am heating ofet by teducing the current (1R increases with I squased thus increasing the power and the enrgy

iven egavalent arrangement heatfing elements 3R 3R 3 R 3R Rea 3R R equivalent incuit tor heatiy- R Heat hransferred to water in 5hours Mars o watesxspecific heat waterxAT 6-95-J T ニ(00°F-3·77e R00°F= 9333'c Heat Sooo gallons = So00x3-8L = 19000L density &ater -1000 kg/m 1kg/1L ASs ume Mass 6 Loater= 19, 000 ka 1000 Heat energy water 1900ox4185.8x(93.33-39-73) 441869912J Vt 200 TAS resistan ce varies with Hme 1000 Qz0x 3600x.5x2- 35.19355 200°F 4418693912x10 Ro'F RroooF = 28.6 853R 35 1+0.004x(93-33 -37-99) 1+08T II00'F 120x312.57A 929-88 eadr element at 100 125I 4.194 Cuerent tr ough Votage avoss each element 20V 4. 4o m eash eloment YI120X419500W