1. Principle of a D.C. ammeter

A D.C. ammeter (such as a moving-coil galvanometer based meter) is designed to measure current in one fixed direction. Its deflection is proportional to the average torque, and hence to the average current through it.

2. Nature of alternating current

In alternating current, $i = I_0 \sin \omega t$ Over one complete cycle, the current is positive for one half-cycle and negative for the next half-cycle.

3. Average value over a complete cycle

The average current over one full cycle is $I_{\text{avg}} = \frac{1}{T}\int_0^T I_0 \sin \omega t\, dt = 0$ So the positive and negative halves cancel each other.

4. Effect on D.C. ammeter

Since the D.C. ammeter responds to the average value of current, and for A.C. over a complete cycle this average is zero, it gives no proper reading for alternating current.

5. Checking options

• A: Average value of current for complete cycle is zero → Correct.
• B: A.C. changes direction → This is true, but not the best direct reason in terms of meter reading. The meter fails because the average over a cycle is zero.
• C: A.C. cannot pass through D.C. ammeter → False. A.C. can pass through, but the meter will not measure it properly.
• D: D.C. ammeter will get damaged → False in general.

Therefore, the correct option is: $\boxed{A}$