Transformer efficiency/primary current (help )

[wakefreak90]

Transformer efficiency/primary current (help!)

Real transformers are not 100% efficient. That is, the efficiency, in percent, is represented by e = (100%) Ps/Pp. A step-down transformer has an efficiency of 92.5% is used to obtain 23.0 V from the 125 V household voltage. The current in the secondary circuit is 27.0 A. What is the current in the primary circuit?

I have tried basically everything but I cannot seem to figure it out. Help?

 

[LowlyPion]

If it was 100% efficient what current would need to be supplied?

That means the power in is the power out.

So what is the power out?

Once you know the power in then you know that it needed to be more by how much? .92 of actual Power = Power you calculated as required to meet the statement of the problem.

 

[nlightner]

I would approach this problem by using the basic principles of transformers and electrical circuits. Firstly, we need to understand that transformers work on the principle of electromagnetic induction, where a changing magnetic field induces a voltage in a conductor. This voltage is then used to transfer energy from the primary circuit to the secondary circuit.

In this scenario, the efficiency of the transformer is given as 92.5%. This means that only 92.5% of the power supplied to the primary circuit (Pp) is transferred to the secondary circuit (Ps). The remaining 7.5% is lost as heat and other losses. We can represent this mathematically as:

e = (100%) Ps/Pp
92.5% = (100%) Ps/Pp
0.925 = Ps/Pp

Next, we can use Ohm's Law to relate the voltage, current, and resistance in a circuit. In this case, we know that the voltage in the secondary circuit (Vs) is 23.0 V and the current is 27.0 A. We also know that the voltage in the primary circuit (Vp) is 125 V, but we don't know the current in the primary circuit (Ip). So we can write the following equation:

Vs = Vp * (Ps/Pp) = 23.0 V
27.0 A = 125 V * (Ps/Pp)

Now, we can rearrange this equation to solve for Ps/Pp:

Ps/Pp = 27.0 A / 125 V
Ps/Pp = 0.216

Substituting this value for Ps/Pp in our previous equation, we get:

0.925 = 0.216
0.925 = Pp * 0.216

Finally, we can solve for Pp by dividing both sides by 0.216:

Pp = 0.925 / 0.216
Pp = 4.28 A

Therefore, the current in the primary circuit is 4.28 A. This means that for every 4.28 amps of current flowing through the primary circuit, 92.5% of that power will be transferred to the secondary circuit. I hope this helps you understand the relationship between transformer efficiency and primary current.