A 1250 W radiant heater is constructed to operate at 115 V. (a) What is the current in the heater when the unit is operating? (b) What is the resistance of the heating coil? (c) How much thermal energy is produced in 1.0 h?
The power or rate of energy transfer, in an electrical device across which a potential difference is equal to the product of current and potential difference. It can also be defined as energy transferred per unit time.
By using the equation for the rate of electrical energy transferred, Ohm’s law, and the thermal energy, we can find the current in the heater when the unit is operating, the resistance of the heating coil, and the thermal energy.
The rate of the electrical energy transferred, P = iV …(i)
Here, P is the power, i is current, V is the potential difference.
According to Ohm’s law, the potential difference is given by, V = iR …(ii)
Here, R is the resistance
The thermal energy E is generated by the heater, E = Pt …(iii)
Here, t is the time.
Using the given data in equation (i), we can get the value of the current flowing into the heater as follows:
Hence, the value of the current is 10.9 A.
Using the given data in equation (ii), we can get the value of the resistance in the heating coils as follows:
Hence, the value of the resistance is .
The thermal energy E is generated by the heater in time t = 3600s is given using the data substituted in equation (iii) as follows:
Hence, the amount of produced thermal energy is .
A fuse in an electric circuit is a wire that is designed to melt, and thereby open the circuit, if the current exceeds a predetermined value. Suppose that the material to be used in a fuse melts when the current density rises to . What diameter of cylindrical wire should be used to make a fuse that will limit the current to 0.50 A?
A block in the shape of a rectangular solid has a cross-sectional area of 3.50cm2 across its width, a front-to-rear length of 15.8cm , and a resistance of . The block’s material contains conduction electrons/m3. A potential difference of 35.8 V is maintained between its front and rear faces. (a) What is the current in the block? (b) If the current density is uniform, what is its magnitude? What are (c) the drift velocity of the conduction electrons and (d) the magnitude of the electric field in the block?
A cylindrical metal rod is 1.60 m long and 5.50 m in diameter. The resistance between its two ends (at ) is . (a) What is the material? (b) A round disk, 2.00 cm in diameter and 1.00 mm thick, is formed of the same material. What is the resistance between the round faces, assuming that each face is an equi-potential surface?
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