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CE Predict/Explain An electric space heater has a power
Chapter 21, Problem 90GP(choose chapter or problem)
Problem 90GP
CE Predict/Explain An electric space heater has a power rating of 500 W when connected to a given voltage V.
(a) If two of these heaters are connected in series to the same voltage, is the power consumed by the two heaters greater than, less than, or equal to 1000 W? (b) Choose the best explanation from among the following:
I. Each heater consumes 500 W; therefore two of them will consume 500 W + 500 W = 1000 W.
II. The voltage is the same, but the resistance is doubled by connecting the heaters in scries. Therefore, the power consumed (P = V2/R) is less than 1000 W.
III. Connecting two heaters in series doubles the resistance. Since power depends on the resistance squared, it follows that the power consumed is greater than 1000 W.
Questions & Answers
QUESTION:
Problem 90GP
CE Predict/Explain An electric space heater has a power rating of 500 W when connected to a given voltage V.
(a) If two of these heaters are connected in series to the same voltage, is the power consumed by the two heaters greater than, less than, or equal to 1000 W? (b) Choose the best explanation from among the following:
I. Each heater consumes 500 W; therefore two of them will consume 500 W + 500 W = 1000 W.
II. The voltage is the same, but the resistance is doubled by connecting the heaters in scries. Therefore, the power consumed (P = V2/R) is less than 1000 W.
III. Connecting two heaters in series doubles the resistance. Since power depends on the resistance squared, it follows that the power consumed is greater than 1000 W.
ANSWER:
Solution 90GP
Step 1 of 3
(a)
Here we need to find whether two of the heaters with power rating each are connected in series with the same voltage
, will consume the power which is greater, lesser or equal to
.
The electric heater can be considered as simple resistor with certain resistance.
In the given case, when the two identical heaters are connected in series, the total resistance of the circuit doubles whereas the voltage remains constant.