How Much Energy is Stored in Hair Dryer Heating Coils?
What is the total self-inductance of the heating coils assuming they act like a single solenoid?
(a) How much energy is stored in them when 10.0 A flows through?
(c) What is the average amount in mV required to shut them off in 4.17 ms?
Answer:
(a) The total self-inductance of the heating coils is approximately 0.051 H.
(b) The energy stored in the coils when 10.0 A flows through them is approximately 25.5 J.
(c) The average amount in mV required to shut them off in 4.17 ms is not provided in the data.
The heating coils in a hair dryer are described as having a diameter of 0.800 cm, a combined length of 100 m, and a total of 395 turns. To find the total self-inductance of the coils, we can use the formula for the self-inductance of a solenoid:
L = (μ₀N²A) / l,
where:
L is the self-inductance,
μ₀ is the permeability of free space (4π x 10⁻⁷ H/m),
N is the total number of turns (395 turns),
A is the cross-sectional area of one coil (πr²),
l is the length of the solenoid (100 m).
By calculating the cross-sectional area A and applying the formula, we find that the total self-inductance of the heating coils is approximately 0.051 H. The energy stored in the coils when a current of 10.0 A flows through them can be calculated using the energy formula and yields about 25.5 J.