For a transformer with a turns ratio of 10:1, the secondary current is approximately how many times the primary current in an ideal transformer?

For a transformer with a turns ratio of 10:1, the secondary current is approximately how many times the primary current in an ideal transformer?

• A. About 1/10 as large
• B. About the same
• C. About 10 times higher
• D. About 100 times higher

Answer: (C)

In an ideal transformer, power in equals power out: Vp Ip = Vs Is. A turns ratio of 10:1 means the primary has 10 times as many turns as the secondary, so the secondary voltage is one-tenth of the primary: Vs = Vp/10. Substituting into the power balance gives Vp Ip = (Vp/10) Is, which simplifies to Is = 10 Ip. So the secondary current is about 10 times the primary current. The voltage drops by a factor of 10, so current rises by the same factor to keep power constant.

In an ideal transformer, power in equals power out: Vp Ip = Vs Is. A turns ratio of 10:1 means the primary has 10 times as many turns as the secondary, so the secondary voltage is one-tenth of the primary: Vs = Vp/10. Substituting into the power balance gives Vp Ip = (Vp/10) Is, which simplifies to Is = 10 Ip. So the secondary current is about 10 times the primary current. The voltage drops by a factor of 10, so current rises by the same factor to keep power constant.