Alternating current cannot be measured by DC ammeter because
(a) AC cannot pass through DC ammeter
(

Q: Why doesn't the needle of the DC ammeter just vibrate back and forth with the AC?

Standard AC in our homes has a frequency of 50 Hz, meaning it changes direction 100 times a second! The mechanical inertia of the ammeter's needle is too high to follow such rapid vibrations, so it simply stays at the average position, which is zero.

Q: If the average current is zero, does that mean AC doesn't deliver any power?

Not at all! Power depends on the square of the current ($P = I^2 R$). Since the square of a negative number is positive, power is delivered during both the positive and negative half-cycles. This is why we use RMS (Root Mean Square) values for AC.

Q: Can we modify a DC ammeter to measure AC?

Yes! By adding a rectifier circuit (like a diode bridge) before the ammeter, we can convert the alternating current into direct current. The ammeter will then measure the average of this rectified current, which can be calibrated to show the RMS value of the original AC.

Q: What kind of instrument is actually used to measure AC?

We typically use Hot-Wire ammeters or Moving-Iron instruments. These devices work on principles that do not depend on the direction of the current, such as the heating effect ($I^2 R$), allowing them to measure the RMS value directly.

Q: What would happen if we passed a very low-frequency AC (like 1 Hz) through a DC ammeter?

If the frequency is low enough (e.g., 1 cycle per second), the needle's inertia wouldn't be a problem. You would actually see the needle swing to the right, return to zero, swing to the left, and back again, following the slow alternating current!

Question

Alternating current cannot be measured by DC ammeter because

Options:

(A) AC cannot pass through DC ammeter

(B) AC changes direction

(C) average value of current for complete cycle is zero

(D) DC ammeter will get damaged

Sigma Percentile · Accepted Answer

### The Mystery of the Unmoving Needle

Imagine you have a standard DC ammeter, the kind you've used in countless direct current experiments. You connect it to an alternating current (AC) source, expecting the needle to jump and give you a reading. But to your surprise, the needle just sits there, stubbornly pointing at zero. Why does this happen? Is the ammeter broken? Not at all! The secret lies in understanding what a DC ammeter actually measures and the fundamental nature of alternating current.

### What Does a DC Ammeter Measure?

A standard DC ammeter, typically a moving-coil galvanometer, operates on the principle of magnetic torque. When current flows through its coil, it experiences a torque proportional to the current. However, the mechanical system of the needle has inertia. It cannot respond instantly to very rapid changes. Therefore, what the needle actually displays is the **time-averaged value** of the current flowing through it.

### The Nature of Alternating Current

Now, let's look at alternating current. Unlike DC, which flows steadily in one direction, AC is a rebel. It constantly changes its magnitude and reverses its direction periodically. Mathematically, it is represented as a sine wave:

$$I = I_0 \sin(\omega t)$$

During the first half of its cycle, the current flows in the positive direction. If we were to plot this, it forms a positive hump above the time axis. During the second half of the cycle, the current reverses and flows in the negative direction, forming an identical hump below the time axis.

### The Grand Cancellation

Here is where the magic happens. If we want to find the average current over one complete cycle, we need to sum up all the instantaneous values. Geometrically, this is the net area under the current-time graph.

Because the positive half-cycle is perfectly symmetrical to the negative half-cycle, their areas are equal and opposite. When you add them together, they perfectly cancel each other out!

$$I_{avg} = \frac{\int_0^T I_0 \sin(\omega t) dt}{T} = 0$$

Since the average value of alternating current over a complete cycle is exactly **zero**, the DC ammeter, which only responds to the average current, feels no net torque. The rapid pushes and pulls on the coil average out to nothing, and the needle remains at zero. This is why we need special instruments, like hot-wire ammeters, which measure the RMS (Root Mean Square) value based on the heating effect, to accurately measure AC!

Animated Solution for Physics - Alternating Current: Alternating current cannot be measured by DC ammeter because

Select Answer:

Visualized Solution

DC Ammeter Principle

AC Waveform

Positive Half Cycle

Negative Half Cycle

Average Current

Conclusion

The Sigma Insight: Alternating Current (AC) and Voltage

The Mystery of the Unmoving Needle

What Does a DC Ammeter Measure?

The Nature of Alternating Current

The Grand Cancellation

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