A hair dryer with a plastic casing uses a coiled wire as a heat source - Leaving Cert Physics - Question 8 - 2010

1. Magnetic effect: An electric current generates a magnetic field around the conductor.
2. Chemical effect: An electric current can cause chemical reactions, such as electrolysis.

When switch A is closed, the circuit is completed, allowing current to flow. Adjusting the rheostat changes the resistance in the circuit, which in turn modifies the speed of the fan by controlling the amount of current flowing to the motor.

When both switches A and B are closed, current flows through the heating coil, causing it to generate heat. At the same time, the fan operates, blowing the heated air out, which aids in drying.

To find the initial resistance of the coil, we use the formula for power:
$P = I^2 R$
Here, we rearrange it to find R:
$R = \frac{P}{I^2}$
Assuming a maximum power (P) of 2000 W at 230 V:
The current (I) can be derived from Ohm’s law:
$I = \frac{P}{V} = \frac{2000}{230} \approx 8.7 ext{ A}$
Then, substituting the values:
$R = \frac{2000}{(8.7)^2} \approx 26.4 \Omega$

Using the formula for current:
$I = \frac{P}{V} = \frac{2000 ext{ W}}{230 ext{ V}} \approx 8.7 ext{ A}$

To calculate the length of the wire, use the formula for resistance:
$R = \rho \frac{L}{A}$
where:

• $R = 26.4 \Omega$
• $\rho = 1.1 \times 10^{-6} \Omega m$ (resistivity of nichrome)
• $A = \pi r^2$, with diameter 0.17 mm so radius r = 0.085 mm = 0.085 \times 10^{-3} m.
  Calculating the cross-sectional area:
  $A = \pi (0.085 \times 10^{-3})^2 \approx 2.27 \times 10^{-9} m^2$
  Thus, substituting into the resistance formula:
  $26.4 = 1.1 \times 10^{-6} \frac{L}{2.27 \times 10^{-9}}$
  Solving for length L gives:
  $L \approx 0.5448 m$ or 54.48 cm.

If the fan stops working, the airflow that helps dissipate the heat generated by the coil diminishes. Consequently, the coil's temperature rises, increasing its resistance due to the temperature coefficient of resistivity.
Higher resistance leads to a reduction in current, according to Ohm’s law, as the voltage remains constant.