Neon signs require about 12000V for their operation. The primary operates from 120-V 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) 1:100
To find the ratio of the number of loops in the secondary to the number of loops in the primary (a), we can use the formula:
Number of loops in secondary (Ns) / Number of loops in primary (Np) = Voltage in secondary (Vs) / Voltage in primary (Vp)
Given that the voltage in the secondary (Vs) is 12000V and the voltage in the primary (Vp) is 120V, we can substitute these values into the formula:
Ns / Np = 12000V / 120V
Simplifying the equation, we get:
Ns / Np = 100
Therefore, the ratio of the number of loops in the secondary to the number of loops in the primary is 100:1.
To find the ratio of the power delivered to the secondary coil to the power supplied by the primary coil (b), we can use the formula:
Ratio of power delivered (Ps) / power supplied (Pp) = (Voltage in secondary)^2 / (Voltage in primary)^2
Given that the voltage in the secondary (Vs) is 12000V and the voltage in the primary (Vp) is 120V, we can substitute these values into the formula:
Ps / Pp = (12000V)^2 / (120V)^2
Ps / Pp = 144000000 / 14400
Simplifying the equation, we get:
Ps / Pp = 10000
Therefore, the ratio of the power delivered to the secondary coil to the power supplied by the primary coil is 10000:1.
To answer these questions, we need to use the principles of transformer operation. Transformers work based on the concept of electromagnetic induction, where a changing magnetic field induces voltage in a nearby coil of wire.
a) The ratio of the number of loops in the secondary coil to the number of loops in the primary coil is known as the turns ratio (N2/N1), where N2 represents the number of loops in the secondary, and N1 represents the number of loops in the primary.
In this case, we know that the primary operates from 120-V lines, and neon signs require about 12000V for their operation. Since the primary voltage is 120V and the secondary voltage is 12000V, we can determine the turns ratio using the voltage ratio.
Turns ratio (N2/N1) = Secondary voltage (V2) / Primary voltage (V1)
Turns ratio (N2/N1) = 12000V / 120V
Therefore, the turns ratio is 100, meaning that there are 100 times more loops in the secondary coil than in the primary coil.
b) The ratio of the power delivered to the secondary coil to the power supplied by the primary coil is known as the power ratio (P2/P1), where P2 represents the power delivered to the secondary and P1 represents the power supplied by the primary.
To calculate the power ratio, we can use the turns ratio. Since power is directly proportional to voltage squared, we can square the turns ratio to determine the power ratio.
Power ratio (P2/P1) = (Turns ratio)^2 = (N2/N1)^2
Power ratio (P2/P1) = (100)^2 = 10000
Therefore, the power delivered to the secondary coil is 10000 times greater than the power supplied by the primary coil.
By using the principles of transformer operation and the given voltages, we can determine the ratios of loops and power between the primary and secondary coils.