Transformer current relation: a step-down transformer has a turns ratio of 5:1 (primary:secondary). If the secondary current is 1 A rms, what is the primary current (assume ideal behavior)?

Introduction / Context:
Transformers exchange voltage and current according to their turns ratio. In an ideal transformer, power is conserved (ignoring losses), so an increase in current on one side corresponds to a decrease on the other when voltage is stepped down or up. This question reinforces the current relationship given a known turns ratio and measured secondary current.

Given Data / Assumptions:

• Turns ratio N_p : N_s = 5 : 1 (step-down).
• Secondary current I_s = 1 A rms.
• Ideal transformer (no losses): V_p * I_p ≈ V_s * I_s.

Concept / Approach:
For an ideal transformer, voltage ratio equals turns ratio: V_p / V_s = N_p / N_s. Current ratio is the inverse: I_p / I_s = N_s / N_p. Therefore I_p = I_s * (N_s / N_p). With N_p/N_s = 5, N_s/N_p = 1/5, so the primary current is one-fifth of the secondary current in this step-down case.

Step-by-Step Solution:
Identify ratios: N_p/N_s = 5/1.Use current relation: I_p = I_s * (N_s / N_p).Compute: I_p = 1 A * (1 / 5) = 0.2 A.Select 0.2 A.

Verification / Alternative check:
Voltage is stepped down by 5, current stepped up by 5 on the secondary (relative to primary). Since I_s is larger, the primary must carry less current: 0.2 A is consistent with power balance (V down by 5, I up by 5, P roughly constant).

Why Other Options Are Wrong:
0.3 A, 0.4 A, and 0.6 A do not follow the exact inverse ratio of 5:1 and would violate ideal power conservation given the stated secondary current. “None” is incorrect because 0.2 A is correct.

Common Pitfalls:
Confusing which side is primary vs secondary; using the same ratio for both voltage and current; ignoring that real transformers have losses but the ideal relation is still the design baseline.

Final Answer:
0.2 A