A) 2.Use a step_down transformer with N2/N1= 1/2.
We have:
- Input voltage of the electrical outlet: [tex]V_1 = 240 V[/tex]
- Output voltage desired for using the hair blower: [tex]V_2 = 120 V[/tex]
So, in order to use the hair blower, we need to decrease the voltage. This can be done by using a step-down transformer, which has a larger number of turns in its primary coil compared to the secondary coil. The transformer equation states that:
[tex]\frac{V_2}{V_1}=\frac{N_2}{N_1}[/tex]
where
[tex]N_1[/tex] is the number of turns in the primary coil
[tex]N_2[/tex] is the number of turns in the secondary coil
here we have
[tex]\frac{V_2}{V_1}=\frac{120 V}{240 V}=\frac{1}{2}[/tex]
So, the transformer we need to use should have
[tex]\frac{N_2}{N_1}=\frac{1}{2}[/tex]
(b) 7.08 A
In a transformer, the power input is equal to the output power. So we can write:
[tex]P_1 = P_2[/tex]
where
[tex]P_1[/tex] is the power drawn from the outlet
[tex]P_2[/tex] is the power put out from the hair blower
Here we know
[tex]P_2 = 1700 W[/tex]
So we have
[tex]P_1 = 1700 W[/tex]
and we can rewrite the power as product of the voltage times the current:
[tex]P_1 = V_1 I_1[/tex]
since we know also [tex]V_1 = 240 V[/tex], we can find the current drawn from the outlet:
[tex]I_1 = \frac{P_1}{V_1}=\frac{1700}{240}=7.08 A[/tex]
(c) [tex]16.9 \Omega[/tex]
The resistance that the blower will appear to have when operated at 240 V can be found by using the formula:
[tex]P=\frac{V_{rms}^2}{R}[/tex] (1)
where:
P = 1700 W is the power
[tex]V_{rms}[/tex] is the rms voltage
R is the resistance
We use the rms voltage instead of the peak voltage (240 V) because the current in the outlet is an AC current. The rms voltage is given by
[tex]V_{rms}=\frac{V_{max}}{\sqrt{2}}=\frac{240 V}{\sqrt{2}}=169.7 V[/tex]
So now we can re-arrange eq.(1) to find the apparent resistance:
[tex]R=\frac{V_{rms}^2}{P}=\frac{(169.7)^2}{1700}=16.9 \Omega[/tex]
Re-arranging the equation, we can solve to find the resistance:
