Ammeter Loading Effect — Why the Formula Holds
The ammeter loading effect occurs because an ideal ammeter has zero resistance, but a real ammeter has non-zero internal resistance (RA). When you insert it into a circuit to measure current, it changes the circuit's total resistance — and therefore the actual current flowing.
Let's understand why the key formula emerges.
1. The Core Idea
Consider a simple circuit: a voltage source V in series with a load resistor RL.
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Without ammeter:
Current Itrue=RLV
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With ammeter (internal resistance RA) inserted in series:
Total resistance becomes RL+RA
Measured current Imeasured=RL+RAV
Since RA>0, we get Imeasured<Itrue.
This reduction is the loading effect.
2. Key Formula — Percentage Error
The percentage error due to loading is:
% error=ItrueItrue−Imeasured×100
Substitute the expressions:
% error=RLVRLV−RL+RAV×100
Simplify step-by-step:
=RLVV(RL1−RL+RA1)×100
=RL1RL1−RL+RA1×100
- Multiply numerator and denominator by RL:
=(1−RL+RARL)×100
- Combine into single fraction:
=RL+RARL+RA−RL×100
% error=RL+RARA×100
3. Why This Formula Makes Sense
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If RA≪RL (ammeter resistance negligible):
% error≈0 — no loading.
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If RA≈RL:
Error is about 50% — serious loading.
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If RA≫RL:
Error approaches 100% — ammeter almost blocks the current. …