Voltmeter Loading and Ammeter Shunt on the Calibration Bench
A calibration bench is checking a 20 V DC supply that feeds a precision divider made of two 100 kΩ, 0.1 % resistors in series; the tap should be 10.00 V. Technician A uses an analog multimeter on its 10 V range, sensitivity 20 kΩ/V, and reads 8.0 V. Technician B uses a handheld DMM with a 10 MΩ input impedance and reads 9.95 V. Technician A concludes the divider resistors are out of tolerance. The same bench also needs a 10 A ammeter range added to a 1 mA, 50 Ω moving-coil movement, and the workshop wants the new range to read correctly to within 1 %.
1. Calculate the true tap voltage, predict what each meter should read, and decide whether the resistors are faulty.
Read the worked answer
The true tap, unloaded, is 20 × 100k/(100k + 100k) = 10.00 V.
Analog meter input resistance = 10 V × 20 kΩ/V = 200 kΩ. The lower resistor becomes 100k || 200k = 66.7 kΩ:
V = 20 × 66.7 / (100 + 66.7) = 20 × 66.7/166.7 = 8.00 V
DMM: 100k || 10 MΩ = 99.01 kΩ, so V = 20 × 99.01/199.01 = 9.95 V.
Both readings match the loading calculation exactly. The resistors are in tolerance; Technician A measured the meter's own resistance in parallel with the divider. The 8 V reading is a 20 % loading error on a 100 kΩ source. Using the analog meter's 50 V range (1 MΩ) would give 100k || 1M = 90.9 kΩ and about 9.52 V, still 4.8 % low. The correct conclusion is instrument loading, not component failure.
2. Design the 10 A shunt for the 1 mA, 50 Ω movement and state the practical construction requirements.
Read the worked answer
At full-scale deflection the movement needs:
V_m = Im × Rm = 1 mA × 50 Ω = 50 mV
The shunt carries the rest of the current, 10 − 0.001 ≈ 9.999 A, and must drop the same 50 mV:
R_sh = 0.050 / 9.999 ≈ 5.0 mΩ
Shunt dissipation = I²R = 100 × 0.005 = 0.5 W, so specify at least a 2 W manganin or constantan element to limit temperature drift - copper would change resistance with self-heating and destroy the 1 % target. Use a four-terminal (Kelvin) connection so the lead and contact resistance do not add to 5 mΩ; solder the voltage taps directly on the shunt body. Check the burden voltage (50 mV) is acceptable in the 10 A circuit and that the meter leads plus shunt stay under the 1 % error budget.
3. The workshop wants all future low-current measurements on this bench to be trustworthy to 1 %. Recommend a measurement procedure, including how to handle the analog meter if it must be used.
Read the worked answer
The dominant error is voltmeter loading, so the first rule is to compare the meter's input resistance with the source resistance. The DMM's 10 MΩ is about 100 times the 100 kΩ divider, giving only 1 % shunting - borderline for a 1 % budget, and it still explains the 9.95 V vs 10.00 V gap. For better than 1 %, buffer the tap with a unity-gain op-amp or use a 10 MΩ+ meter and apply the divider correction.
If the analog meter must be used, take the reading on the highest range that still gives adequate deflection, and correct it:
V_true = V_read × (R_meter + R_source)/R_meter
For 8.0 V on the 200 kΩ range with a 100 kΩ source: 8.0 × 300/200 = 12 V, which shows how poor the raw reading is - so correction alone is not acceptable practice.
Finally, verify the DMM's calibration certificate and record range, resolution and input impedance with every measurement so the loading error is auditable.