Transformer turns ratio and voltage/current calculations

[Prototype]

1) A transformer is designed to change 120 V into 10,000 V, and there are 5,000 turns in the primary. How many turns are in the secondary, assuming 100 perfect efficiency?

2) A transformer has 420 turns in the primary and 120 in the secondary. What kind of transformer is this and, assuming 100 percent efficiency, by what factor does it change the voltage? By what factor does it change the current?

 

[vsage]

1) The product of the potential and number of turns should be the same coming in as going out of the transformer.

2) I'm not sure what 420 has to do with anything, but household outlets in the US are 120V (it's different in Europe, careful!). Consider also that voltage is directly proportional to current by ohm's first law V = IR.

 

[thepatientmental]

1) To calculate the number of turns in the secondary, we can use the equation Np/Ns = Vp/Vs, where Np is the number of turns in the primary, Ns is the number of turns in the secondary, Vp is the voltage in the primary, and Vs is the voltage in the secondary. We can rearrange this equation to solve for Ns, which gives us Ns = (Np * Vs)/Vp. Plugging in the given values of Np = 5000, Vp = 120 V, and Vs = 10,000 V, we get Ns = (5000 * 10,000)/120 = 416,666.67 turns in the secondary. This assumes 100% efficiency, meaning all the energy is transferred from the primary to the secondary without any losses.

2) This is a step-up transformer, as the number of turns in the secondary is greater than the primary. To calculate the voltage and current factors, we can use the equations Vs/Vp = Ns/Np and Is/Ip = Np/Ns, where Vs is the voltage in the secondary, Vp is the voltage in the primary, Is is the current in the secondary, and Ip is the current in the primary. Plugging in the given values of Np = 420, Ns = 120, and assuming 100% efficiency, we get Vs/Vp = 120/420 = 0.2857 and Is/Ip = 420/120 = 3.5. This means that the voltage is stepped up by a factor of 0.2857 and the current is stepped down by a factor of 3.5 in this transformer.