In an ideal transformer, which relationships hold between primary and secondary voltages, currents, and turns?

In an ideal transformer, which relationships hold between primary and secondary voltages, currents, and turns?

• A. Vp/Vs = Np/Ns; Ip/Is = Np/Ns; power is not conserved
• B. Vp/Vs = Ns/Np; Ip/Is = Ns/Np; power conserved
• C. Vp/Vs = Np/Ns; Ip/Is = Ns/Np; power conserved: Vp Ip = Vs Is
• D. Vp/Vs = Ns/Np; Ip/Is = Np/Ns; power conserved

Answer: (C)

In an ideal transformer, the voltages scale with the turns on each winding, while the currents scale inversely, so that power is preserved across the device. Specifically, the primary-to-secondary voltage ratio matches the turns ratio: Vp/Vs = Np/Ns. Because power must stay the same (no losses in an ideal case), Vp Ip = Vs Is. Using this energy balance, the current ratio must be the inverse of the voltage ratio: Ip/Is = Ns/Np. Put together, all three relationships hold consistently: voltage follows the turns, current adjusts inversely, and power remains constant. If you tried to reverse the voltage or current ratios, you’d violate either the turn-to-voltage link or the energy balance, and saying power isn’t conserved contradicts the ideal model.

In an ideal transformer, the voltages scale with the turns on each winding, while the currents scale inversely, so that power is preserved across the device. Specifically, the primary-to-secondary voltage ratio matches the turns ratio: Vp/Vs = Np/Ns. Because power must stay the same (no losses in an ideal case), Vp Ip = Vs Is. Using this energy balance, the current ratio must be the inverse of the voltage ratio: Ip/Is = Ns/Np. Put together, all three relationships hold consistently: voltage follows the turns, current adjusts inversely, and power remains constant. If you tried to reverse the voltage or current ratios, you’d violate either the turn-to-voltage link or the energy balance, and saying power isn’t conserved contradicts the ideal model.