A 1200 W hair dryer is designed for 117 v.
a) What will be the percentage change in power output if the voltage drops to 105 v.
b) How would the actual change in resistivity with temperature affect your answer.
a) To find the percentage change in power output when the voltage drops, we need to calculate the power output at both the initial voltage of 117 V and the decreased voltage of 105 V.
The power output (P) of a device can be calculated using the formula:
P = V * I,
where P is power in watts (W), V is voltage in volts (V), and I is current in amperes (A).
Given that the hair dryer is designed for 117 V and has a power output of 1200 W, we can calculate the current:
P = V * I
1200 W = 117 V * I
Rearranging the equation, we find:
I = 1200 W / 117 V
I ≈ 10.26 A
Now, let's calculate the power output at 105 V:
P = 105 V * 10.26 A
P ≈ 1076.3 W
To find the percentage change, we can use the formula:
Percentage Change = (New Value - Initial Value) / Initial Value * 100
Using this formula for the power output:
Percentage Change = (1076.3 W - 1200 W) / 1200 W * 100
Percentage Change ≈ -10.3%
Therefore, the percentage change in power output when the voltage drops to 105 V is approximately -10.3%.
b) The actual change in resistivity with temperature can affect the answer because it can impact the relationship between voltage and current. If the resistivity increases with temperature, it means the current will be lower for the same voltage.
In this case, a change in resistivity with temperature would result in a lower current at the decreased voltage of 105 V, further reducing the power output compared to the initial calculation.
However, without specific information about the resistivity-temperature relationship or the material used in the hair dryer's heating element, it is challenging to quantify the exact effect. Understanding the resistivity-temperature relationship and how it affects current would be essential for a more accurate analysis.
a) To calculate the percentage change in power output, we can use the formula:
Percentage change = ((New value - Old value) / Old value) * 100
Given that the hair dryer is designed for 117 V and the power is 1200 W, let's calculate the power output at 105 V.
Old power = 1200 W
Old voltage = 117 V
New voltage = 105 V
Using the formula: P = V^2 / R, we can find the resistance (R) of the hair dryer.
Old resistance:
R = V^2 / P = (117 V)^2 / 1200 W ≈ 11.45 Ω
New resistance:
R' = (105 V)^2 / P = 9.94 Ω
Now, let's calculate the percentage change in power output.
Percentage change = ((New value - Old value) / Old value) * 100
= ((105 V)^2 / (117 V)^2 - 1) * 100
≈ ((9.94 Ω / 11.45 Ω) - 1) * 100
≈ (0.866 - 1) * 100
≈ -13.4%
Therefore, if the voltage drops to 105 V, the power output of the hair dryer would decrease by approximately 13.4%.
b) The change in resistivity with temperature should not affect the answer because we are assuming that the voltage drop is due to a change in the power supply and not a change in the ambient temperature. However, if the temperature were to change significantly, it could affect the resistivity of the material and thereby impact the calculations.
a) Since power = V^2/R , if R were constant the power would decrease by a factor (105/117)^2 = 0.0805. This is a 19.5% reduction in power
b) The electric heater wire in a hair dryer does not have a constant resistance with temperature. The resistance will be somewhat lower at the lower temperature that goes with the reduced voltage. This will raise the power somewhat from the value predicted in part (a)