Why does a meter change the circuit?

The same divider reads lower after connection

Connect two resistors of twenty kilohms each across a supply of ten volts. Their midpoint starts at $5\,\mathrm V$ above the return. Connect the probes to the midpoint and return. With an input resistance of two hundred kilohms, the ideal resistor network gives a reading of about $4.76\,\mathrm V$.

The change comes from current inside the meter. Connecting it puts another branch beside the lower resistor, and the source current divides differently. The source can deliver more current overall even as less current flows through the original load resistor. The indication describes that new distribution.

These are chosen teaching resistances evaluated with circuit laws. Increasing both resistances in the divider makes the disturbance from the same meter more pronounced. The relationship between the input resistance and the circuit resistance matters to the result.

Sources: [1]

A pointer needs a little current

A moving-coil meter sends a small current through wire in a magnetic field. Opposite sides feel opposite forces that turn the coil and its attached pointer. A spring winds up until its restoring torque balances the magnetic torque. Curved pole faces make the field approximately radial, pointing along the local radius, over the movement range, which helps keep deflection proportional to coil current.

That current still has to come from the measured circuit. A voltage input uses a large resistance to limit it. At a given voltage, a larger input resistance draws less current. The difference matters particularly when the source itself has a large resistance.

Sources: [2][1]

A range switch changes the current path

One small movement can cover several voltage ranges. A higher range places more resistance in series with the coil so that the current stays small. With a fixed current needed to reach the end of the scale, a higher voltage range therefore has a larger input resistance. The Simpson manual describes a DC sensitivity of twenty thousand ohms per volt. That is a terminal relationship, not the resistance of the bare coil.

For a current range, a low resistance sits beside the coil. Most of the terminal current passes through this shunt, leaving a small fraction in the movement. The combined input resistance is low, but inserting it into the circuit still costs voltage. The drop across the entire input path is the burden voltage.

For another teaching example, a supply of one volt and a load of one kilohm carry $1\,\mathrm{mA}$ before meter insertion. Add one hundred ohms and the current falls to about $0.909\,\mathrm{mA}$. A path of ten ohms gives about $0.990\,\mathrm{mA}$. A more sensitive range can disturb this circuit more.

Sources: [3][1]

A digital detector still has an input network

A digital meter sends an analog signal to an analog-to-digital converter and reports the result as digits. It does not need a rotating coil to carry the indication. Digital voltage inputs can offer very large resistances. The cited Keysight specifications allow ten megohms or a higher resistance on some DC ranges; the value remains specific to the instrument and range.

A ten-megohm input on the earlier divider gives about $4.995\,\mathrm V$, close to the original five volts. The improvement comes from drawing less current. Digital current measurements still use a shunt and a connecting path, so their burden belongs to the complete meter input.

Sources: [4]

Keep calibration and circuit loading together

A zero observation and a known reference convert a pointer angle or an ADC count into a voltage or current. Retaining the range, actual input resistances and contacted nodes with the reading preserves its meaning.

Even with a correct zero and scale, the earlier divider should still read about 4.76 volts: that is the actual voltage after connection. To approach the original five volts, draw less input current, or use a separate circuit calculation to estimate the state before the meter was connected.

Sources: [1]