Q.The resistance of ideal ammeter is -

Ammeter Loading Effect – First Principles

Imagine you want to measure the current flowing through a bulb in a simple circuit. You take an ammeter, break the wire, and insert the meter in series. The reading you get — is it the original current that was flowing before you touched the circuit? Not exactly. The moment you insert the ammeter, you have added a small extra resistance into the path. That extra resistance changes the total resistance of the circuit, and therefore changes the current itself.

This is the core intuition: the act of measuring changes the thing being measured.

The Precise Statement

Why It Happens – Step by Step

Consider a simple circuit: a battery of voltage $V$ and a load resistor $R_L$. The true current (without any meter) is:

Now you insert an ammeter with internal resistance $R_m$ in series. The total resistance becomes $R_L + R_m$, so the measured current is:

Since $R_m > 0$, we always have $I_{\text{measured}} < I_{\text{true}}$.

The percentage error due to loading is:

When Does It Matter Most?

• Low-resistance circuits (e.g., measuring current in a power supply line): $R_L$ is small, so even a small $R_m$ (say 0.1 Ω) can cause noticeable error.
• High-precision measurements: In labs or instrumentation, even 1% error may be unacceptable.
• Digital multimeters (DMMs) typically have very low $R_m$ (milliohms) on current ranges, so loading is minimal for most practical circuits. But analog moving-coil meters can have higher $R_m$, especially on low current ranges.

How to Minimise Loading

1. Use an ammeter with the lowest possible internal resistance — ideally zero, but practically as small as possible.
2. Choose a higher current range on a multimeter: higher ranges often have lower shunt resistance, hence lower $R_m$.
3. If you know $R_m$, correct the reading using the formula above — but this requires knowing $R_L$ accurately.
4. Use an indirect method: measure voltage across a known precision shunt resistor and calculate current via Ohm’s law (this is what ammeters do internally anyway, but with a very low shunt). …