If the efficiency of a transformer is 100%, which of the following equations would be correct?

Analyze the question: For an ideal (100% efficient) transformer, the power input equals the power output. We need to find which equation follows from this.

Concept:

• Turns ratio: E_s/E_p = N_s/N_p
• Power in = Power out: I_pE_p = I_sE_s

Solution:

From the turns ratio: E_p/E_s = N_p/N_s, so E_p = E_s(N_p/N_s)

Efficiency 100% means: I_pE_p = I_sE_s

Rearranging gives: I_p/I_s = E_s/E_p = N_s/N_p

So I_pN_p = I_sN_s, which is the same as N_sI_s = N_pI_p.

Check each option:

• A. N_pE_p = N_sE_s. This is wrong, because the correct relation is N_p/E_p = N_s/E_s, i.e. N_pE_s = N_sE_p.
• B. N_sI_p = N_pI_s. This is wrong, because it gives I_p/I_s = N_p/N_s, which is inverted.
• C. N_sI_s = N_pI_p. This is correct, as derived above.
• D. I_pE_s = I_sE_p. This is wrong, because the correct relation is I_pE_p = I_sE_s.

Tip: In an ideal transformer, current is inversely proportional to the number of turns (and to the voltage). So the product "turns × current" is the same on both sides: N_pI_p = N_sI_s. Remember that voltage and turns go together, while current goes the opposite way.