Neon signs require about 12000V for their operation. The primary operates from 120V lines.
a. What is the ratio of the number of loops in the secondary to the number of loops in the primary?
b. What is the ratio of the power delivered to the secondary coil to the power supplied by the primary coil?
I will be happy to critique your thinking.
a. 100:1
b. 100:1
Are these correct?
How do you get the power supplied if you don't know the resistance?
To answer these questions, we need to apply the principles of transformers and calculate the ratios involved.
a. The ratio of the number of loops in the secondary to the number of loops in the primary, also known as the turns ratio, can be determined using the voltage ratio. In a transformer, the voltage ratio is equal to the turns ratio. The voltage ratio is given as 12000V (secondary) to 120V (primary).
So, the turns ratio (T) can be calculated using the formula:
T = V_secondary / V_primary
T = 12000V / 120V
T = 100
Therefore, the turns ratio or the ratio of the number of loops in the secondary to the number of loops in the primary is 100:1.
b. The power delivered to the secondary coil can be calculated using the formula:
P_secondary = (V_secondary^2) / R
The power supplied by the primary coil can be calculated using the formula:
P_primary = (V_primary^ 2) / R
The power delivered to the secondary coil can be determined as a fraction of the power supplied by the primary coil, which gives us the power ratio.
So, the power ratio (P_ratio) can be calculated using the formula:
P_ratio = P_secondary / P_primary
P_ratio = [(V_secondary^2) / R] / [(V_primary^2) / R]
Since the resistance (R) is the same for both primary and secondary circuits, it cancels out in the equation.
P_ratio = (V_secondary^2) / (V_primary^2)
P_ratio = (12000V^2) / (120V^2)
P_ratio = (12000^2) / (120^2)
P_ratio = 100^2
P_ratio = 10000
Therefore, the power ratio or the ratio of the power delivered to the secondary coil to the power supplied by the primary coil is 1:10000.